Mathematical trigonometry and special angiological knowledge!

The special angle refers to the trigonometric value of the degree angle in a right triangle, the opposite side of 30° is half of the hypotenuse, and the opposite side of 45° is equal to the edge of the forest, and according to these conditions, you can deduce the trigonometric value yourself.

Hello, my answer is: sin2a=2sina 6 1cosa

cos2a=cosa^2-sina^2=1-2sina^2=2cosa^2-1

tan2a=2tana (1-tana 2) sine double angle formula:

sin2α = 2cosαsinα

Derivation: sin2a=sin(a+a)=sinacosa+cosinaina=2sinacosa

Extended formula: sin2a = 2sinacosa = 2tanacosa 2 = 2tana [1+tana 2].

Cosine double angle formula:

The formula for cosine double angle has three sets of representations, and three sets of forms are equivalent:

Derivation: cos2a=cos(a+a)=cosacosa-sinasina=(cosa) 2-(sina) 2=2(cosa) 2-1

1-2(sina)^2

Tangent double angle formula:

tan2α=2tanα/[1-(tanα)^2]

Derivation: tan2a = tan(a+a) = (tana + tana) (1-tanatana) = 2tana [1-(tana) 2].

Thank you for your cooperation!

There are many students who can't remember the trigonometric value of a special angle =0°(0): sin =0, cos =1, tan =0

30°(π/6)：sinα=1/2，cosα=√3/2，tanα=√3/3

45°(π/4)：sinα=√2/2，cosα=√2/2，tanα=1

60°(π/3)：sinα=√3/2，cosα=1/2，tanα=√3

90°(π/2)：sinα=1，cosα=0

The sinusoidal values of the three angles of 30°, 45°, and 60°.

The common denominator with the cosine value is the denominator.

are all 2, if the numerators are added with the root number, then the number of squares will be 1, 2, 3Tangent.

The characteristic is that all the numerators are marked with the root number, so that the denominator value is 3, then the corresponding number of squares is 3, 9, 27.

Thirty, four, five, sixty degrees, trigonometric functions are firmly remembered;

The denominator string is cut into three, and the numerator should add the root number;

One, two, three, three, two, one, cut value of three nine twenty-seven;

Increasing tangent and sine, cosine functions.

To decrement.

Special trigonometric values generally refer to trigonometric values at 30°, 45°, and 60° isoangles.

Trigonometric function is one of the basic elementary functions, which is a function that takes the angle (the most commonly used radian system in mathematics, the same round of the Lie segment) as the independent variable, and the angle corresponds to the coordinate of the terminal edge of any angle and the intersection point of the unit circle or its ratio as the dependent variable. It can also be defined equivalently in terms of the length of the various line segments related to the unit circle.

Trigonometric functions play an important role in the study of the properties of geometric shapes such as triangles and circles, and are also a fundamental mathematical tool for the study of periodic phenomena. In mathematical analysis, trigonometric functions are also defined as infinite series or solutions to specific differential equations, allowing their values to be extended to arbitrary real values, even complex values.

Common trigonometric functions include sine, cosine, and tangent. In other disciplines such as navigation, surveying and mapping, and engineering, other trigonometric functions such as cotangent function, secant function, cosecant function, sagittal function, cosagittal function, semi-sagittal function, semi-cosagittal function, and other trigonometric functions are also used. The relationship between different trigonometric functions can be determined by geometrical intuition, or by calculation, and is called trigonometric identities.

Trigonometric functions are generally used to calculate the edges of unknown lengths and unknown angles in triangles, and have a wide range of uses in navigation, engineering, and physics. In addition, using trigonometric functions as a template, similar functions such as Zen can be fixed, which are called hyperbolic functions. The common hyperbolic function is also known as hyperbolic sine function, hyperbolic cosine function, and many more.

Special trigonometric values generally refer to trigonometric values at 30°, 45°, and 60° isoangles. Trigonometric values for these angles are often used. And by using the trigonometric formula of the sum and difference of two angles, the trigonometric values of some other angles can be found.

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, cos60° = 1 2, tan60° = root number 3; sin90°=1，cos90°=0。

Unit Circle Definition:

It can also be defined in terms of a unit circle with a radius of 1 and a center as the origin. The unit circle definition has no great value in practical calculations; In fact, for most angles it depends on right triangles.

But the unit circle definition does allow trigonometric functions to have definitions for all positive and negative radiant angles, not just for angles between 0 and 2 radians. It also provides an image that contains all the important trigonometric functions. According to the Pythagorean theorem, the equation for a unit circle is:

For any point on the circle (x,y), x +y = 1.