# How to find the trigonometric formula table for any angle

### What are the trigonometric formulas for arbitrary angles

Mastering the internal laws and the nature of trigonometric functions is also the key to learning trigonometric functions, the next to share the trigonometric formulas for arbitrary angles, together with the specific content.

Trigonometric formula for an arbitrary angle

Assuming α is an arbitrary angle, the trigonometric formula for an arbitrary angle is:

sin(2kπ+α)=sinα(k∈Z)

cos(2kπ+α)=cosα(k∈Z)

tan(2kπ+α)=tanα(k∈Z)

Trigonometric derivatives

Sine function: (sinx)’=cosx

Cosine function: (cosx)’=-sinx

Tangent function: (tanx)’=sec²x

Cosidic function: (cotx)’=-csc²x

Cotangent function: (secx)’=tanx- secx

Cositive cut function: (cscx)’=-cotx-cscx

Trigonometric transformation formula

sin(-α)=-sinα

cos(-α)=cosα

sin(π/2-α)=cosα

cos(π/2-α)=sinα

< p>sin(π/2+α)=cosα

cos(π/2+α)=-sinα

sin(π-α)=sinα

cos(π-α)=-cosα

sin(π+α)=-sinα

tanα=sinα/cosα

tan(π/2 + α) = -cotα

tan(π/2 – α) = cotα

tan(π – α) = -tanα

tan(π + α) = tanα

The universal formula for trigonometric functions

sin(a)=[2tan(a/2)]/[1+tan2(a/2)]

cos(a)=[1-tan2(a/2)]/[1+tan2(a/2)]

tan(a)=[2tan(a/2)]/[1-tan2(a/2)]

### Trigonometry full formulas

Trigonometry formulas include product to sum difference formula, sum to product formula, triple angle formula, sine to double angle formula, cosine to double angle formula, and cosine theorem.

1 productization and difference formula. sinα-cosβ=(1/2)*[sin(α+β)+sin(α-β)]; cosα-sinβ=(1/2)*[sin(α+β)-sin(α-β)]; cosα-cosβ=(1/2)*[cos(α+β)+cos(α-β)]; sinα- sinβ=-(1/2)*[cos(α+β)-cos(α-β)]

2, sum and difference product formula. sinα+sinβ=2sin[(α+β)/2]-cos[(α-β)/2];sinα-sinβ=2cos[(α+β)/2]-sin[(α-β)/2]cosα+cosβ= 2cos[(α+β)/2]-cos[(α-β)/2];cosα-cosβ=-2sin[(α+β)/2]-sin[(α-β)/2]

3Triple angle equations. sin3α=3sinα-4sin^3α:cos3α=4cos^3α-3cosα

4Sum and Difference of two angles The trigonometric relationships sin(α+β)=sinαcosβ+cosαsinβ;sin(α-β)=sinαcosβ-cosαsinβ;cos(α+β)=cosαcosβ-sinαsinβ;cos(α-β)=cosαcosβ+sinαsinβ;tan(α+β)=(tanα+ tanβ)/(1-tanα-tanβ);tan(α-β)=(tanα-tanβ)/(1+tanα-tanβ)

### A complete list of trigonometric formulas

1. Formula 1: Let α be any angle, and the values of the same trigonometric function for angles with the same terminal side are equal sin(2kπ+α)=sinα(k∈Z). (2) cos(2kπ+α) = cosα (k ∈ Z). (3) tan(2kπ+α)=tanα(k∈Z) cot(2kπ+α)=cotα(k∈Z). 2. Equation 2: Setting α to be an arbitrary angle, the relationship between the trigonometric value of π+α and the trigonometric value of α. (1) sin(π+α)=-sinα.

Trigonometric functions (also called “circular functions”) are functions of angles; they are important in the study of triangles and in modeling periodic phenomena and many other applications. Trigonometric functions are usually defined as the ratio of the two sides of a right triangle containing the angle, or equivalently, as the lengths of various line segments on the unit circle.

### Trigonometric function angle formula

Trigonometric function angle formula: sin(A+B)=sinAcosB+cosAsinB; cos(A+B)=cosAcosB-sinAsinB; tan(A+B)=(tanA+tanB)/(1-tanAtanB).

Related information:

1. The trigonometric and angle formula, also known as the addition theorem for trigonometric functions, is a relationship in which the trigonometric functions of the sum (difference) of several angles are expressed through the trigonometric functions of each of those angles.

2, right triangle ABC: angle A sine (sin) is equal to the opposite side of angle A than the hypotenuse, sina = y/r, sine of the inverse of the secant (sec); cosine (cos) is equal to the neighboring side of the angle A than the hypotenuse, cosa = x/r, the inverse of the cosine of the cosine of the cotangent (csc); tangent (tan) is equal to the opposite side of the neighboring side of tana = y/x. The inverse of tangent is cotangent (cot).

3. Common trigonometric functions include the sine, cosine, and tangent functions. In other disciplines such as navigation, surveying and mapping, engineering and other trigonometric functions such as cotangent function, tangent function, cotangent function, cosine function, cosine function, half-sine function, half-cosine function and other trigonometric functions are also used.

4, trigonometric function is one of the basic elementary functions, is the angle (most commonly used in mathematics radian system, the same below) as the independent variable, the angle corresponds to any angle of the final side and the unit of the coordinates of the intersection point of the circle, or the ratio of its function as the dependent variable. It can also be equivalently defined in terms of the lengths of the various line segments associated with the unit circle.