Memory skills: odd variable pairs are unchanged, and symbols are in quadrant [2]. That is, if the shape is (2k+ 1) 90 α, the function name becomes a function with a remainder, sine becomes cosine, cosine becomes sine, tangent becomes cotangent, and cotangent becomes tangent. If the shape is 2k×90 α, the function name remains unchanged.
The meaning of the inductive formula formula "even if it changes strangely, the symbol will look at the quadrant";
Trigonometric function value of k ×π/2 A (k ∈ z). (1) When k is an even number, it is equal to the trigonometric function value of the same name of α, and a symbol is added in front to indicate the original trigonometric function value when α is regarded as an acute angle;
(2) When k is an odd number, different trigonometric function values equal to α are preceded by a sign of the original trigonometric function value when α is regarded as an acute angle.
Memory method 1: parity is unchanged, and symbols look at quadrants:
Memory method 2: No matter how big the angle is, take α as an acute angle.
Take inductive formula 2 as an example:
If α is regarded as an acute angle (the terminal edge is in the first quadrant), π+α is the angle of the third quadrant (the terminal edge is in the third quadrant), the function value of sine function is negative in the third quadrant, the function value of cosine function is negative in the third quadrant, and the function value of tangent function is positive in the third quadrant. In this way, the inductive Formula 2 is obtained.
Take the inductive formula 4 as an example:
If α is regarded as an acute angle (the terminal edge is in the first quadrant), π-α is the angle of the second quadrant (the terminal edge is in the second quadrant), the trigonometric function value of sine function is positive in the second quadrant, the trigonometric function value of cosine function is negative in the second quadrant, and the trigonometric function value of tangent function is negative in the second quadrant.
Application of inductive formula;
General steps of transforming trigonometric functions by induction;
Special reminder: knowledge reserves needed for trigonometric function simplification and evaluation: ① memorizing trigonometric function values from special angles; ② Pay attention to the flexible application of inductive formulas; ③ The requirements of trigonometric function simplification are the least number of terms, the least number of times, the least function name, the simplest denominator and the best evaluation.