What are the special trigonometric function values?

sin120=sin60 cos120=-cos60 .sin105 = 15 degrees and 75 degrees can be used by the sum difference formula of the angle. sin(a+b)=cosasinb+ degree can be substituted with 45 degrees 30 degrees, and 75 degrees can be substituted with 45 degrees 30 degrees.

sin105=sin(60+45)=sin60cos45+cos60sin45

sin15=sin(45-30)=sin45cos30-cos45sin30

sin75=sin(45+30)=sin45cos30+cos45sin30

sin120=sin(180-120)=sin60 are all special trigonometric values after conversion, which can be easily calculated, and the same is true for cosine.

It's just that cos120 = -cos(180-120) = -cos60

Special trigonometric values.

Generally refers to trigonometric values at 30°, 45°, 60° isoangles. Trigonometric values for these angles are often used. And make use of the trigonometric formula of the sum and difference of two angles.

Trigonometric values for some other angles can be found.

By comparison, it can be found that it is more than ** triangle.

There is a strong symmetry in relation to the trigonometric values, and the proof of these values can be achieved with the help of the proportions in the triangle.

Special trigonometric value table

0° sinα=0 cosα=1 tαnα=0 cotα→∞secα=1 cscα→∞

15°(π12) sinα=(6-√2)/4 cosα=(6+√2)/4 tαnα=2-√3 cotα=2+√3 secα=√6-√2 cscα=√6+√2

sinα=√2-√2)/2 cosα=√2+√2)/2 tαnα=√2-1 cotα=√2+1 secα=√4-2√2) cscα=√4+2√2)

30°(π6) sinα=1/2 cosα=√3/2 tαnα=√3/3 cotα=√3 secα=2√3/3 cscα=2

45°(π4) sinα=√2/2 cosα=√2/2 tαnα=1 cotα=1 secα=√2 cscα=√2

60°(π3) sinα=√3/2 cosα=1/2 tαnα=√3 cotα=√3/3 secα=2 cscα=2√3/3

sinα=√2+√2)/2 cosα=√2-√2)/2 tαnα=√2+1 cotα=√2-1 secα=√4+2√2) cscα=√4-2√2)

75°(5 12) sin =(6+ 2) 4 cos =(6- 2) 4 t n =2+ 3 cot =2- 3 sec = 6+ bureau filial piety 2 csc = 6- 2

90°(π2) sinα=1 cosα=0 tαnα→∞cotα=0 secα→∞cscα=1

180°(πsinα=0 cosα=-1 tαnα=0 cotα→∞secα=-1 cscα→∞

270°(3π/2) sinα=-1 cosα=0 tαnα→∞cotα=0 secα→∞cscα=-1

360°(2π) sinα=0 cosα=1 tαnα=0 cotα→∞secα=1 cscα→∞

The above content refers to the Encyclopedia of Eyeing Years - Special Trigonometric Values.

Trigonometric values for special angles: sin0°=0, cos0°=1, tan0°=0;sin30°=1 2,cos30°=root32,tan30°=root333;sin45°=root2 2,cos45°=root22,tan45°=1;sin60° = root number 3 2, town lead base cos60 ° = 1 2, tan60 ° = root number 3; sin90°=1，cos90°=0。

Special trigonometric values.

Generally refers to the sine and Cosine at the angle of 0, 30°, 45°, 60°, 90°, 180°.

Value. Trigonometric excitation values for these angles are often used. And make use of the trigonometric formula of the sum and difference of two angles.

Trigonometric values for some other angles can be found.

Trigonometric functions

0°sinα=0cosα=1 tαnα=0cotα→∞secα=1cscα→∞

15°( 12) sin =(6- 2) 4 cos =(6+ 2) 4 t n =2- 3 cot =2+ 3 sec = 6- gojin2 csc = 6+ 2

sinα=√2-√2)/2 cosα=√2+√2)/2 tαnα=√2-1 cotα=√2+1 secα=√4-2√2) cscα=√4+2√2)

30°(π6) sinα=1/2 cosα=√3/2 tαnα=√3/3 cotα=√3 secα=2√3/3 cscα=2

45°(π4) sinα=√2/2 cosα=√2/2 tαnα=1 cotα=1 secα=√2 cscα=√2

75°(5π/12) sinα=(6+√2)/4 cosα=(6-√2)/4 tαnα=2+√3 cotα=2-√3 secα=√6+√2 cscα=√6-√2

90°(π2) sinα=1 cosα=0 tαnα→∞cotα=0 secα→∞cscα=1

180°(πsinα=0 cosα=-1 tαnα=0 cotα→∞secα=-1 cscα→∞

360°(2π) sinα=0 cosα=1 tαnα=0 cotα→∞secα=1 cscα→∞

SpecialTrigonometric valuesIt's like a mess of oranges:

1. sin0°=0

2. cos0°=1

3. tan0°=0

Fourth, sin30 ° = 1 2

5. COS30° = root number 3 2

6. tan30 ° = root number 3 3

7. sin45 ° = root number 2 2

8. COS45° = root number 2 2

Jiuqihuai, tan45°=1

10. sin60° = root number 3 2

11. COS60°=1 2

12. tan60° = root number 3

13. sin90°=1

14. cos90°=0

Special trigonometric values generally refer to trigonometric values at 30°, 45°, and 60° isoangles. Trigonometric values for these angles are often used. And make use of the trigonometric formula of the sum and difference of two angles.

Trigonometric values for some other angles can be found.

Trigonometric function is one of the basic elementary functions, which is measured in terms of angles (mathematically the most common terrestrial tremor is in radians.

The same hereinafter) is the independent variable, and the angle corresponds to the coordinate of the final edge of any angle and the intersection point of the unit circle or its ratio is a function of the dependent variable. It can also be defined equivalently by the length of various line segments related to the unit circle.

Trigonometric functions are used in the study of triangles.

and the properties of geometric shapes, such as circles, play an important role and are also fundamental mathematical tools for the study of periodic phenomena.

Trigonometric Origins:

Early research on trigonometric functions can be traced back to ancient times. Ancient Greece.

The founder of trigonometry was Hipparchus in the 2nd century BC. He followed ancient Babylon.

It is the practice of dividing the circumference into 360 equal parts (i.e., the radian of the circumference is 360 degrees, which is different from the modern radian system). For a given radian, he gives the corresponding string length value, which is the same as the modern sine function.

is equivalent. Hipparchus actually gave the earliest table of trigonometric functions. However, trigonometry in ancient Greece was basically spherical trigonometry.

This has to do with the fact that the main body of study of the ancient Greeks was astronomy. Menelaus used sine in his book Sphericalism to describe Menelaus's theorem for spheres.

Ancient Greece and its application of astronomy in Ptolemy in Egypt.

The era reached its peak in the Mathematical Compilation

syntaxis mathematica) calculates the sine values of the angle of 36 degrees and angles of 72 degrees, and also gives the formula for calculating the sum angle and the formula for half the angle.

method. Ptolemy also gave the sinusoidal values corresponding to all integer and semi-integer radians from 0 to 180 degrees.

The above content referenceEncyclopedia - Special trigonometric values.

<> "Special Functions Trigonometric Functions include Sine Function, Cosine Function, Tangent Function, Cotangent Function, Cant Function, Cosecant Function, Arcsine Function, Inverse Reduction Cosine Function, Arctangent Function, Inverse Cotangent Function, etc.

Special functions refer to some mathematical functions that have special properties. In trigonometric functions, there are some special function values that can be obtained by specific angles or special conditions. Here are some common special function values and their corresponding angles or conditions:

1.sin(0) = 0: The value of the sinusoidal function is 0 at an angle of 0.

2.sin( 6) = 1 2: The value of the sinusoidal function at an angle of 6 (or 30°) is 1 2.

3.sin( 4) = 1 2: The value of the sinusoidal function at an angle of 4 (or 45°) is 1 2.

4.sin( 3) =3 2: The value of the sinusoidal function at an angle of 3 (or 60°) is 3 2.

5.sin( 2) = 1: The value of the sinusoidal function at an angle of 2 (or 90°) is 1.

In addition to the sine function, there are also some special function values for the cosine function and the tangent function, as follows:

1.cos(0) = 1: The value of the cosine function at an angle of 0 is 1.

2.cos( 6) =3 2: The value of the cosine function at an angle of 6 (or 30°) is 3 2.

3.cos( 4) = 1 2: The value of the cosine function at an angle of 4 (or 45°) is 1 2.

4.cos( 3) = 1 2: The value of the cosine function at an angle of 3 (or 60°) is 1 2.

5.cos( 2) = 0: The value of the cosine function at an angle of 2 (or 90°) is 0.

1.tan(0) =0: The tangent function has a value of 0 at an angle of 0.

2.tan( 6) = 1 3: The tangent function has a value of 1 3 at an angle of 6 (or 30°).

3.tan( 4) =1: The tangent filial piety function has a value of 1 at an angle of 4 (or 45°).

4.tan( 3) =3: The tangent function has a value of 3 at an angle of 3 (or 60°). Crack Shen Huai.

5.tan( 2) = infinity: The tangent function has an infinite value at an angle of 2 (or 90°).

These special function values are often used in the calculation and application of trigonometric functions, and being familiar with them can facilitate our mathematical calculations and derivations.

A special function is a function that has a special property or a special expression in mathematics. In trigonometric functions, there are several common special function values:

1.Sine function:

Special function values for sinusoidal functions include:

sin(0) =0

sin(π/6) =1/2

sin(π/4) =2/2

sin(π/3) =3/2

sin(π/2) =1

2.Cosine function:

Special function values for cosine functions include:

cos(0) =1

cos(π/6) =3/2

cos(π/4) =2/2

cos(π/3) =1/2

cos(π/2) =0

3.Tangent function:

The values of the tangent function of the positive special function include:

tan(0) =0

tan(π/4) =1

tan(π/6) =3/3

tan(π/3) =3

tan( 2) = infinity (non-existent).

These special function values are often used in the calculation and application of trigonometric functions. It is important to note that trigonometric functions are periodic, so these special function values can be generalized to other angles across the number line through periodicity.