Degree measure of angle. Radian measure of angle. Converting degrees to radians and vice versa.

Attention!
There are additional
materials in Special Section 555.
For those who are very "not very..."
And for those who “very much…”)

In the previous lesson we learned how to measure angles on a trigonometric circle. Learned how to count positive and negative angles. We learned how to draw an angle greater than 360 degrees. It's time to figure out how to measure angles. Especially with the number "Pi", which strives to confuse us in tricky tasks, yes...

Standard tasks Trigonometry with the number "Pi" is solved well. Visual memory helps. But any deviation from the template is a disaster! To avoid falling - understand necessary. Which is what we will do now with success. I mean, we’ll understand everything!

So, what do angles count? In the school trigonometry course, two measures are used: degree measure of angle And radian angle measure. Let's look at these measures. Without this, there is nowhere in trigonometry.

Degree measure of angle.

We somehow got used to degrees. At the very least we passed geometry... And in life we ​​often come across the phrase “turned 180 degrees,” for example. A degree, in short, is a simple thing...

Yes? Answer me then what is a degree? What, it doesn’t work out right away? That's it...

Degrees were invented in Ancient Babylon. It was a long time ago... 40 centuries ago... And they came up with a simple idea. They took and divided the circle into 360 equal parts. 1 degree is 1/360 of a circle. That's all. They could have broken it into 100 pieces. Or 1000. But they divided it into 360. By the way, why exactly 360? How is 360 better than 100? 100 seems to be somehow smoother... Try to answer this question. Or weak against Ancient Babylon?

Somewhere at the same time, in Ancient Egypt they were tormented by another question. How many times is the length of a circle greater than the length of its diameter? And they measured it this way, and that way... Everything turned out to be a little more than three. But somehow it turned out shaggy, uneven... But they, the Egyptians, are not to blame. After them, they suffered for another 35 centuries. Until they finally proved that no matter how finely you cut a circle into equal pieces, from such pieces you can make smooth the length of the diameter is impossible... In principle, it is impossible. Well, how many times the circumference is greater than the diameter was established, of course. Approximately. 3.1415926... times.

This is the number "Pi". So shaggy, so shaggy. After the decimal point there is an infinite number of numbers without any order... Such numbers are called irrational. This, by the way, means that from equal pieces of a circle the diameter smooth don't fold. Never.

For practical use, it is customary to remember only two digits after the decimal point. Remember:

Since we understand that the circumference of a circle is greater than its diameter by “Pi” times, it makes sense to remember the formula for the circumference of a circle:

Where L- circumference, and d- its diameter.

Useful in geometry.

For general education, I’ll add that the number “Pi” is found not only in geometry... In various branches of mathematics, and especially in probability theory, this number appears constantly! By itself. Beyond our desires. Like this.

But let's return to degrees. Have you figured out why in Ancient Babylon the circle was divided into 360 equal parts? And not by 100, for example? No? OK. I'll give you a version. You can’t ask the ancient Babylonians... For construction, or, say, astronomy, it is convenient to divide the circle into equal parts. Now figure out what numbers it is divisible by completely 100, and which ones - 360? And in what version of these divisors completely- more? This division is very convenient for people. But...

As it turned out much later than Ancient Babylon, not everyone likes degrees. Higher mathematics does not like them... Higher mathematics is a serious lady, organized according to the laws of nature. And this lady declares: “Today you broke the circle into 360 parts, tomorrow you will break it into 100, the day after tomorrow into 245... And what should I do? No, really...” I had to listen. You can't fool nature...

We had to introduce a measure of angle that did not depend on human inventions. Meet - radian!

Radian measure of angle.

What is a radian? The definition of a radian is still based on a circle. An angle of 1 radian is an angle that cuts an arc from a circle whose length is ( L) is equal to the length of the radius ( R). Let's look at the pictures.

Such a small angle, it’s almost non-existent... We move the cursor over the picture (or touch the picture on the tablet) and we see about one radian. L = R

Do you feel the difference?

One radian is much more than one degree. How many times?

Let's look at the next picture. On which I drew a semicircle. The unfolded angle is, naturally, 180°.

Now I'll cut this semicircle into radians! We hover the cursor over the picture and see that 180° fits 3 and a half radians.

Who can guess what this tail is equal to!?

Yes! This tail is 0.1415926.... Hello, number "Pi", we haven't forgotten you yet!

Indeed, 180° degrees contains 3.1415926... radians. As you yourself understand, writing 3.1415926 all the time... is inconvenient. Therefore, instead of this infinite number, they always write simply:

But on the Internet the number

It’s inconvenient to write... That’s why I write his name in the text - “Pi”. Don't get confused, okay?...

Now we can write down an approximate equality in a completely meaningful way:

Or exact equality:

Let's determine how many degrees are in one radian. How? Easily! If there are 180° degrees in 3.14 radians, then there are 3.14 times less in 1 radian! That is, we divide the first equation (the formula is also an equation!) by 3.14:

This ratio is useful to remember. One radian is approximately 60°. In trigonometry, you often have to estimate and assess the situation. This is where this knowledge helps a lot.

But the main skill of this topic is converting degrees to radians and vice versa.

If the angle is given in radians with the number "Pi", everything is very simple. We know that "Pi" radians = 180°. So we substitute radians for “Pi” - 180°. We get the angle in degrees. We reduce what is reduced, and the answer is ready. For example, we need to find out how many degrees in angle "Pi"/2 radian? So we write:

Or, a more exotic expression:

Easy, right?

The reverse translation is a little more complicated. But not much. If the angle is given in degrees, we must figure out what one degree is equal to in radians and multiply that number by the number of degrees. What is 1° equal to in radians?

We look at the formula and realize that if 180° = “Pi” radians, then 1° is 180 times smaller. Or, in other words, we divide the equation (a formula is also an equation!) by 180. There is no need to represent “Pi” as 3.14; it is always written with a letter anyway. We find that one degree is equal to:

That's all. We multiply the number of degrees by this value and get the angle in radians. For example:

Or, similarly:

As you can see, in a leisurely conversation with lyrical digressions, it turned out that radians are very simple. And the translation is no problem... And “Pi” is a completely tolerable thing... So where does the confusion come from!?

I'll reveal the secret. The fact is that in trigonometric functions the degrees symbol is written. Always. For example, sin35°. This is sine 35 degrees . And the radian icon ( glad) - not written! It's implied. Either mathematicians were overwhelmed by laziness, or something else... But they decided not to write. If there are no symbols inside the sine-cotangent, then the angle is in radians ! For example, cos3 is the cosine of three radians .

This leads to confusion... A person sees “Pi” and believes that it is 180°. Anytime and anywhere. By the way, this works. For the time being, the examples are standard. But "Pi" is a number! The number is 3.14, but not degrees! This is "Pi" radians = 180°!

Once again: “Pi” is a number! 3.14. Irrational, but a number. Same as 5 or 8. You can, for example, do about "Pi" steps. Three steps and a little more. Or buy "Pi" kilograms of candy. If an educated seller comes across...

"Pi" is a number! What, did I annoy you with this phrase? Have you already understood everything long ago? OK. Let's check. Tell me, which number is greater?

Or what is less?

This is one of a series of slightly non-standard questions that can drive you into a stupor...

If you, too, have fallen into a stupor, remember the spell: “Pi” is a number! 3.14. In the very first sine it is clearly stated that the angle is in degrees! Therefore, it is impossible to replace “Pi” by 180°! "Pi" degrees is approximately 3.14°. Therefore, we can write:

There are no notations in the second sine. So, there - radians! This is where replacing “Pi” by 180° will work just fine. Converting radians to degrees, as written above, we get:

It remains to compare these two sines. What. forgot how? Using a trigonometric circle, of course! Draw a circle, draw approximate angles of 60° and 1.05°. Let's see what sines these angles have. In short, everything is described as at the end of the topic about the trigonometric circle. On a circle (even the crooked one!) it will be clearly visible that sin60° significantly more than sin1.05°.

We will do exactly the same thing with cosines. On the circle, draw angles of approximately 4 degrees and 4 radian(Have you forgotten what 1 radian is approximately equal to?). The circle will say everything! Of course, cos4 is less than cos4°.

Let's practice using angle measures.

Convert these angles from degrees to radians:

360°; 30°; 90°; 270°; 45°; 0°; 180°; 60°

You should get these values ​​in radians (in a different order!)

0

By the way, I specifically highlighted the answers in two lines. Well, let's figure out what the corners are in the first line? At least in degrees, at least in radians?

Yes! These are the axes of the coordinate system! If you look at the trigonometric circle, then the moving side of the angle with these values fits exactly on the axes. These values ​​​​need to be known. And I noted the angle of 0 degrees (0 radians) for good reason. And then some people just can’t find this angle on a circle... And, accordingly, they get confused in the trigonometric functions of zero... Another thing is that the position of the moving side at zero degrees coincides with the position at 360°, so there are always coincidences on the circle near.

In the second line there are also special angles... These are 30°, 45° and 60°. And what's so special about them? Nothing special. The only difference between these angles and all the others is that you should know about these angles All. And where they are located, and what trigonometric functions these angles have. Let's say the value sin100° you don't have to know. A sin45°- please be so kind! This is mandatory knowledge, without which there is nothing to do in trigonometry... But more about this in the next lesson.

In the meantime, let's continue training. Convert these angles from radian to degree:

You should get results like this (in disarray):

210°; 150°; 135°; 120°; 330°; 315°; 300°; 240°; 225°.

Happened? Then we can assume that converting degrees to radians and back- no longer your problem.) But translating angles is the first step to understanding trigonometry. There you also need to work with sines and cosines. And with tangents and cotangents too...

The second powerful step is the ability to determine the position of any angle on a trigonometric circle. Both in degrees and radians. I will give you boring hints about this very skill throughout trigonometry, yes...) If you know everything (or think you know everything) about the trigonometric circle, and the measurement of angles on the trigonometric circle, you can check it out. Solve these simple tasks:

1. Which quarter do the angles fall into:

45°, 175°, 355°, 91°, 355° ?

Easily? Let's continue:

2. Which quarter do the corners fall into:

402°, 535°, 3000°, -45°, -325°, -3000°?

No problem too? Well, look...)

3. You can place the corners in quarters:

Could you? Well, you give..)

4. Which axes will the corner fall on:

and corner:

Is it easy too? Hm...)

5. Which quarter do the corners fall into:

And it worked!? Well, then I really don’t know...)

6. Determine which quarter the corners fall into:

1, 2, 3 and 20 radians.

I will give an answer only to the last question (it’s a little tricky) of the last task. An angle of 20 radians will fall in the first quarter.

I won’t give the rest of the answers, not out of greed.) Simply, if you haven't decided something you doubt it as a result, or spent on task No. 4 more than 10 seconds, you are poorly oriented in a circle. This will be your problem in all of trigonometry. It’s better to get rid of it (the problem, not trigonometry!) immediately. This can be done in the topic: Practical work with the trigonometric circle in section 555.

It tells you how to solve such tasks simply and correctly. Well, these tasks have been solved, of course. And the fourth task was solved in 10 seconds. Yes, it’s been decided that anyone can do it!

If you are absolutely confident in your answers and you are not interested in simple and trouble-free ways of working with radians, you don’t have to visit 555. I don’t insist.)

A good understanding is a good enough reason to move on!)

If you like this site...

By the way, I have a couple more interesting sites for you.)

You can practice solving examples and find out your level. Testing with instant verification. Let's learn - with interest!)

You can get acquainted with functions and derivatives.

(pi / 4) in three ways.

First.
This method is most often used when solving trigonometric equations in school. It consists of using , which contains the values ​​of four trigonometric functions of the most common arguments.

Such tables exist in several versions. They differ in that the angle values ​​are presented in degrees, radians, or both degrees and radians (which is most convenient).
In the table we find the angle (in this case pi / 4) and the desired function (we need the cosine function) and at the intersection of these values ​​we get the number root of 2 / 2.
Mathematically it is written like this:

Second.
Also a common method that can always be used if there is no table. Is to use (or trigonometric circle).


On such a trigonometric circle, the cosine values ​​are located on the horizontal axis - the abscissa axis, and the arguments - on the curve of the circle itself.
In our case, the cosine argument is equal to pi / 4. Let's determine where this value is located on the circle. Next, we lower the perpendicular to the Ox axis. The value at which the end of this perpendicular ends up will be the value of the given cosine. Therefore, the cosine of pi/4 is equal to the root of 2/2.

Third.
It is also convenient to use the graph of the corresponding function - . It's easy to remember what he looks like.


When using the graph, some knowledge is required to determine the value of the cosine pi/4, which is equal to . In this case, you need to understand that the value of the fraction is greater than 0.5 and less than 1.
There are, of course, several other ways. For example, calculating the cosine value using a calculator. But to do this, you must first convert the angle pi / 4 to degrees. Bradis tables can also be useful.

Table of values ​​of trigonometric functions compiled for angles of 0, 30, 45, 60, 90, 180, 270 and 360 degrees and the corresponding angle values ​​in radians. From trigonometric functions the table shows sine, cosine, tangent, cotangent, secant And cosecant. For the convenience of solving school examples of meaning trigonometric functions in the table are written in the form of a fraction while preserving the signs of extracting the square root of numbers, which very often helps to reduce complex mathematical expressions. For tangent And cotangent Some angles cannot be determined. For values tangent And cotangent There is a dash in the table of values ​​of trigonometric functions for such angles. It is generally accepted that tangent And cotangent of such angles equals infinity. On a separate page there are formulas for reducing trigonometric functions.

The table of values ​​for the trigonometric sine function shows the values ​​for the following angles: sin 0, sin 30, sin 45, sin 60, sin 90, sin 180, sin 270, sin 360 in degrees, which corresponds to sin 0 pi, sin pi/6 , sin pi/4, sin pi/3, sin pi/2, sin pi, sin 3 pi/2, sin 2 pi in radian measure of angles. School table of sines.

For the trigonometric cosine function, the table shows the values ​​for the following angles: cos 0, cos 30, cos 45, cos 60, cos 90, cos 180, cos 270, cos 360 in degrees, which corresponds to cos 0 pi, cos pi by 6, cos pi by 4, cos pi by 3, cos pi by 2, cos pi, cos 3 pi by 2, cos 2 pi in radian measure of angles. School table of cosines.

The trigonometric table for the trigonometric tangent function gives values ​​for the following angles: tg 0, tg 30, tg 45, tg 60, tg 180, tg 360 in degree measure, which corresponds to tg 0 pi, tg pi/6, tg pi/4, tg pi/3, tg pi, tg 2 pi in radian measure of angles. The following values ​​of the trigonometric tangent functions are not defined tan 90, tan 270, tan pi/2, tan 3 pi/2 and are considered equal to infinity.

For the trigonometric function cotangent in the trigonometric table the values ​​of the following angles are given: ctg 30, ctg 45, ctg 60, ctg 90, ctg 270 in degree measure, which corresponds to ctg pi/6, ctg pi/4, ctg pi/3, tg pi/ 2, tan 3 pi/2 in radian measure of angles. The following values ​​of the trigonometric cotangent functions are not defined ctg 0, ctg 180, ctg 360, ctg 0 pi, ctg pi, ctg 2 pi and are considered equal to infinity.

The values ​​of the trigonometric functions secant and cosecant are given for the same angles in degrees and radians as sine, cosine, tangent, cotangent.

The table of values ​​of trigonometric functions of non-standard angles shows the values ​​of sine, cosine, tangent and cotangent for angles in degrees 15, 18, 22.5, 36, 54, 67.5 72 degrees and in radians pi/12, pi/10, pi/ 8, pi/5, 3pi/8, 2pi/5 radians. The values ​​of trigonometric functions are expressed in terms of fractions and square roots to make it easier to reduce fractions in school examples.

Three more trigonometry monsters. The first is the tangent of 1.5 one and a half degrees or pi divided by 120. The second is the cosine of pi divided by 240, pi/240. The longest is the cosine of pi divided by 17, pi/17.

The trigonometric circle of values ​​of the functions sine and cosine visually represents the signs of sine and cosine depending on the magnitude of the angle. Especially for blondes, the cosine values ​​are underlined with a green dash to reduce confusion. The conversion of degrees to radians is also very clearly presented when radians are expressed in terms of pi.

This trigonometric table presents the values ​​of sine, cosine, tangent, and cotangent for angles from 0 zero to 90 ninety degrees at one-degree intervals. For the first forty-five degrees, the names of trigonometric functions should be looked at at the top of the table. The first column contains degrees, the values ​​of sines, cosines, tangents and cotangents are written in the next four columns.

For angles from forty-five degrees to ninety degrees, the names of the trigonometric functions are written at the bottom of the table. The last column contains degrees; the values ​​of cosines, sines, cotangents and tangents are written in the previous four columns. You should be careful because the names of the trigonometric functions at the bottom of the trigonometric table are different from the names at the top of the table. Sines and cosines are interchanged, just like tangent and cotangent. This is due to the symmetry of the values ​​of trigonometric functions.

The signs of trigonometric functions are shown in the figure above. Sine has positive values ​​from 0 to 180 degrees, or 0 to pi. Sine has negative values ​​from 180 to 360 degrees or from pi to 2 pi. Cosine values ​​are positive from 0 to 90 and 270 to 360 degrees, or 0 to 1/2 pi and 3/2 to 2 pi. Tangent and cotangent have positive values ​​from 0 to 90 degrees and from 180 to 270 degrees, corresponding to values ​​from 0 to 1/2 pi and pi to 3/2 pi. Negative values ​​of tangent and cotangent are from 90 to 180 degrees and from 270 to 360 degrees, or from 1/2 pi to pi and from 3/2 pi to 2 pi. When determining the signs of trigonometric functions for angles greater than 360 degrees or 2 pi, you should use the periodicity properties of these functions.

The trigonometric functions sine, tangent and cotangent are odd functions. The values ​​of these functions for negative angles will be negative. Cosine is an even trigonometric function—the cosine value for a negative angle will be positive. Sign rules must be followed when multiplying and dividing trigonometric functions.

Root 2/2 is how much pi?— It happens in different ways (see picture). You need to know which trigonometric function is equal to root two divided by two.

If you liked the post and want to know more, I have more in the works.

cos pi divided by 2

Home > Directory > Mathematical formulas.

Mathematical formulas.

Convert radians to degrees.
A d = A r * 180 / pi

Converting degrees to radians.
A r = A d * pi / 180
Where A d is the angle in degrees, A r is the angle in radians.

Circumference.
L = 2 * pi * R

Length of the arc of a circle.
L=A*R

Area of ​​a triangle.

p=(a+b+c)/2 - semi-perimeter.

Area of ​​a circle.
S = pi * R 2

Sector area.
S = L d * R/2 = (A * R 2)/2

Surface area of ​​the ball.
S = 4 * pi * R 2

S = 2 * pi * R * H

Where S is the area of ​​the lateral surface of the cylinder, R is the radius of the base of the cylinder, H is the height of the cylinder.

S = pi * R * L

S = pi * R * L + pi * R 2

Volume of the ball.
V = 4 / 3 * pi * R 3

Cylinder volume.
V = pi * R 2 * H

Cone volume.

Posted: 01/15/13
Updated: 11/15/14
Total views: 10754
today: 1

Home > Directory > Mathematical formulas.

Egor

Good evening! You asked a very interesting question, I hope we can help you.

How to solve C1. Lesson 2. Unified State Exam in Mathematics 2014

You and I need to solve the following problem: find cos pi divided by 2.
Most often, to solve such problems you need to determine the cosine or sine exponents. For angles from 0 to 360 degrees, almost any value of cos or sin can be easily found in the corresponding plates that exist and are widespread, such as these:

But you and I do not have a sine (sin), but a cosine. Let's first understand what cosine is. Cos (cosine) is one of the trigonometric functions. In order to calculate the cosine of an acute right triangle, you will need to know the ratio of the side of the adjacent angle to the hypotenuse. The cosine pi divided by 2 can be easily calculated using the trigonometric formula, which refers to the standard trigonometry formulas. But if we are talking about the value of the cosine pi divided by 2, then for this we will use the table that we have already mentioned more than once:

Good luck to you in future solutions to similar tasks!
Answer:

Home > Directory > Mathematical formulas.

Mathematical formulas.

Convert radians to degrees.
A d = A r * 180 / pi

Converting degrees to radians.
A r = A d * pi / 180
Where A d is the angle in degrees, A r is the angle in radians.

Circumference.
L = 2 * pi * R
Where L is the circumference, R is the radius of the circle.

Length of the arc of a circle.
L=A*R
Where L is the length of the circular arc, R is the radius of the circle, A is the central angle, expressed in radians
For a circle A = 2*pi (360 degrees), we get L = 2*pi*R.

Area of ​​a triangle.
S = (p * (p-a) * (p-b) * (p-c)) 1/2
Where S is the area of ​​the triangle, a, b, c are the lengths of the sides,
p=(a+b+c)/2 - semi-perimeter.

Area of ​​a circle.
S = pi * R 2
Where S is the area of ​​the circle, R is the radius of the circle.

Sector area.
S = L d * R/2 = (A * R 2)/2
Where S is the area of ​​the sector, R is the radius of the circle, L d is the length of the arc.

Surface area of ​​the ball.
S = 4 * pi * R 2
Where S is the surface area of ​​the ball, R is the radius of the ball.

The lateral surface area of ​​the cylinder.
S = 2 * pi * R * H
Where S is the area of ​​the lateral surface of the cylinder, R is the radius of the base of the cylinder, H is the height of the cylinder.

The total surface area of ​​the cylinder.
S = 2 * pi * R * H + 2 * pi * R 2
Where S is the area of ​​the lateral surface of the cylinder, R is the radius of the base of the cylinder, H is the height of the cylinder.

The area of ​​the lateral surface of the cone.
S = pi * R * L
Where S is the area of ​​the lateral surface of the cone, R is the radius of the base of the cone, L is the length of the generatrix of the cone.

The total surface area of ​​a cone.
S = pi * R * L + pi * R 2
Where S is the total surface area of ​​the cone, R is the radius of the base of the cone, L is the length of the generatrix of the cone.

Volume of the ball.
V = 4 / 3 * pi * R 3
Where V is the volume of the ball, R is the radius of the ball.

Cylinder volume.
V = pi * R 2 * H
Where V is the volume of the cylinder, R is the radius of the base of the cylinder, H is the height of the cylinder.

Cone volume.
V = pi * R * L = pi * R * H/cos (A/2) = pi * R * R/sin (A/2)
Where V is the volume of the cone, R is the radius of the base of the cone, L is the length of the generatrix of the cone, A is the angle at the apex of the cone.

Posted: 01/15/13
Updated: 11/15/14
Total views: 10742
today: 1

Home > Directory > Mathematical formulas.

Egor
You can secure the wire to the terminals of the Crohn battery with a tube cut from the cap of a medical needle.

Table of values ​​of trigonometric functions

Note. This table of trigonometric function values ​​uses the √ sign to represent the square root. To indicate a fraction, use the symbol "/".

see also useful materials:

For determining the value of a trigonometric function, find it at the intersection of the line indicating the trigonometric function. For example, sine 30 degrees - we look for the column with the heading sin (sine) and find the intersection of this table column with the row “30 degrees”, at their intersection we read the result - one half. Similarly we find cosine 60 degrees, sine 60 degrees (once again, at the intersection of the sin column and the 60 degree line we find the value sin 60 = √3/2), etc. The values ​​of sines, cosines and tangents of other “popular” angles are found in the same way.

Sine pi, cosine pi, tangent pi and other angles in radians

The table below of cosines, sines and tangents is also suitable for finding the value of trigonometric functions whose argument is given in radians. To do this, use the second column of angle values. Thanks to this, you can convert the value of popular angles from degrees to radians. For example, let's find the angle of 60 degrees in the first line and read its value in radians under it. 60 degrees is equal to π/3 radians.

The number pi unambiguously expresses the dependence of the circumference on the degree measure of the angle. Thus, pi radians are equal to 180 degrees.

Any number expressed in terms of pi (radians) can be easily converted to degrees by replacing pi (π) with 180.

Examples:
1. Sine pi.
sin π = sin 180 = 0
thus, the sine of pi is the same as the sine of 180 degrees and it is equal to zero.

2. Cosine pi.
cos π = cos 180 = -1
thus, the cosine of pi is the same as the cosine of 180 degrees and it is equal to minus one.

3. Tangent pi
tg π = tg 180 = 0
thus, tangent pi is the same as tangent 180 degrees and it is equal to zero.

Table of sine, cosine, tangent values ​​for angles 0 - 360 degrees (common values)

angle α value (degrees)	angle α value in radians (via pi)	sin (sinus)	cos (cosine)	tg (tangent)	ctg (cotangent)	sec (secant)	cosec (cosecant)
0	0	0	1	0	-	1	-
15	π/12			2 - √3	2 + √3
30	π/6	1/2	√3/2	1/√3	√3	2/√3	2
45	π/4	√2/2	√2/2	1	1	√2	√2
60	π/3	√3/2	1/2	√3	1/√3	2	2/√3
75	5π/12			2 + √3	2 - √3
90	π/2	1	0	-	0	-	1
105	7π/12		-	- 2 - √3	√3 - 2
120	2π/3	√3/2	-1/2	-√3	-√3/3
135	3π/4	√2/2	-√2/2	-1	-1	-√2	√2
150	5π/6	1/2	-√3/2	-√3/3	-√3
180	π	0	-1	0	-	-1	-
210	7π/6	-1/2	-√3/2	√3/3	√3
240	4π/3	-√3/2	-1/2	√3	√3/3
270	3π/2	-1	0	-	0	-	-1
360	2π	0	1	0	-	1	-

If in the table of values ​​of trigonometric functions a dash is indicated instead of the function value (tangent (tg) 90 degrees, cotangent (ctg) 180 degrees), then for a given value of the degree measure of the angle the function does not have a specific value. If there is no dash, the cell is empty, which means we have not yet entered the required value. We are interested in what queries users come to us for and supplement the table with new values, despite the fact that current data on the values ​​of cosines, sines and tangents of the most common angle values ​​is quite sufficient to solve most problems.

Table of values ​​of trigonometric functions sin, cos, tg for the most popular angles
0, 15, 30, 45, 60, 90 ... 360 degrees
(numeric values ​​“as per Bradis tables”)

angle α value (degrees)	angle α value in radians	sin (sine)	cos (cosine)	tg (tangent)	ctg (cotangent)
0	0
15		0,2588	0,9659	0,2679
30		0,5000		0,5774
45		0,7071
		0,7660
60		0,8660	0,5000	1,7321
	7π/18