Finding high trigonometric formulas and reasoning

Quotient relation: sin cos =tan =sec csc cos sin =cot =csc sec squared relation: sin 2( ) cos 2( )=1 1+tan 2( )=sec 2( )1+cot 2( )=csc 2( ) double angle formula.

Sin2a=2sina·cosa cosine i.e. cos2a=cos 2(a)-sin 2(a)=2cos 2(a)-1=1-2sin 2(a) tangent tan2a=(2tana) (1-tan 2(a)) half-angle formula.

tan(a/2)=(1-cosa)/sina=sina/(1+cosa); cot(a/2)=sina/(1-cosa)=(1+cosa)/sina.sin 2(a 2)=(1-cos(a)) 2 cos 2(a 2)=(1+cos(a)) 2 tan(a 2)=(1-cos(a)) sin(a)=sin(a) (1+cos(a)) two angles and formula.

tan( +=(tan +tan ) (1-tan tan ) tan( -=(tan -tan ) (1+tan tan ) cos( +=cos cos -sin sin cos( -=cos cos +sin sin( +=sin cos +cos sin sin( -=sin cos -cos sin sin( -=sin cos -cos sin sin sum of products.

sinαsinβ =-[cos(α+cos(α-/2 cosαcosβ = [cos(α+cos(α-/2 sinαcosβ = [sin(α+sin(α-/2 cosαsinβ = [sin(α+sin(α-/2

Isn't that just the sum difference product or the product and difference formula?

There are many formulas for high school trigonometric functions. Trigonometric function is one of the basic elementary functions, which is a function in which the angle (the most commonly used radian system in mathematics, the same below) 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 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.

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Make a circle and then find the angle, which should be in the textbook.