Trigonometric function is an important content in high school mathematics, and auxiliary angle formula is a very basic and important formula in trigonometric function. The auxiliary angle formula can express trigonometric function of any angle as a simple form, which is convenient for us to calculate and solve problems related to trigonometric function.
The formula of auxiliary angle is: sin (x) = 2tan (x/2)/(1+tan2 (x/2)), cos (x) =1-tan2 (x/2)/(kloc-0/+tan2). These formulas are all formulas with x/2 as the auxiliary angle, so they are called auxiliary angle formulas.
The auxiliary angle formula is widely used. For example, when calculating the value of trigonometric function, we can use the auxiliary angle formula to express trigonometric function of any angle as a simple form. In addition, the auxiliary angle formula can also be used to solve problems related to trigonometric functions, such as solving the maximum, minimum and period of trigonometric functions.
Besides the auxiliary angle formula, there are other important formulas of trigonometric functions in high school mathematics, such as sum and difference angle formula, multiplication sum and difference formula, half angle formula and so on. These formulas are derived to facilitate us to calculate and solve problems related to trigonometric functions.
Auxiliary angle formula is a very important formula in trigonometric function of high school mathematics. It can represent trigonometric functions at any angle as a simple form and can be used to solve problems related to trigonometric functions. By learning and mastering these formulas, we can better understand and apply trigonometric functions, thus solving mathematical problems better.
The formula of trigonometric function includes:
1, the basic relationship of trigonometric functions with the same angle: sin 2 (α)+cos 2 (α) = 1, tanα=sinα/cosα.
2. Inductive formula: Let α be any angle, and the values of the same trigonometric function with the same terminal angle are equal: sin(2kπ+α)=sinα, cos(2kπ+α)=cosα, tan(2kπ+α)=tanα.
3. Sum angle formula: sin(α+β)=sinαcosβ+cosαsinβ, cos(α+β)=cosαcosβ-sinαsinβ, tan (α+β) = (tan α+tan β)/(1-tan α tan β).
4. Differential angle formula: sin(α-β)=sinαcosβ-cosαsinβ, cos(α-β)=cosαcosβ+sinαsinβ, tan (α-β) = (tan α-tan β)/(1+tan α tan β).
5. Sum-product formula: sin θ+sin φ = 2 sin (θ/2+φ/2) cos (θ/2-φ/2), cos θ+cos φ = 2 cos (θ/2+φ/2) cos (θ/2-φ/2), sin θ-sin φ.
6. Sum and difference formula of products: sin θ sin φ =1/2 [-cos (θ+φ)+cos (θ-φ)], cos θ cos φ =1/2 [cos (θ+φ)+cos (θ-φ)], sin θ cos φ.
7. Sine theorem: In any triangle ABC, asinA=bsinB=csinC.
8. Cosine theorem: In any triangle ABC, a 2 = b 2+c 2-2bcosa, b 2 = a 2+c 2-2accosb, c 2 = a 2+b 2-2abcosc.
9. Tangent Theorem: In any triangle ABC, tanA=tanB=tanC.
10, cotangent theorem: cotA+cotB+cotC=0 in any triangle ABC.