Mathematical induction formula 1: Hypothesis? For any angle, the values of the same trigonometric function with the same angle of the terminal edge are equal:
sin(2k？ +? ) = sin? k？ zcos(2k？ +? )=cos？ k？ z
Tan (2k? +? ) = Tan? k？ z
cot(2k？ +? )=cot？ k？ z
Formula 2: set? For any angle, +? What is the trigonometric function value of? The relationship between trigonometric function values is:
Sin (? +? ) =-sin? cos(？ +? )=-cos？
Tan (? +? ) = Tan?
cot(？ +? )=cot？
Formula 3: Any angle? Use-? The relationship between trigonometric function values is:
Sin (-? ) =-sin? cos(-？ )=cos？
Tan (- ) =-Tan?
cot(-？ )=-cot？
Formula 4: Can you get it with Formula 2 and Formula 3? -? With what? The relationship between trigonometric function values is:
Sin (? -? ) = sin? cos(？ -? )=-cos？
Tan (? -? ) =-Tan?
cot(？ -? )=-cot？
Formula 5: Using formula 1 and formula 3, we can get 2? -? With what? The relationship between trigonometric function values is:
Sin (2? -? ) =-sin? cos(2？ -? )=cos？
Tan (2? -? ) =-Tan?
cot(2？ -? )=-cot？
Equation 6:? /2 and? The relationship between trigonometric function values is:
Sin (? /2+? )=cos？ cos(？ /2+? ) =-sin?
Tan (? /2+? )=-cot？
cot(？ /2+? ) =-Tan?
Sin (? /2-? )=cos？
cos(？ /2-? ) = sin?
Tan (? /2-? )=cot？
cot(？ /2-? ) = Tan?
Mathematical induction formula calculation 3? /2 and? The relationship between trigonometric function values is:
Sin (3? /2+? )=-cos？ cos(3？ /2+? ) = sin?
Tan (3? /2+? )=-cot？
cot(3？ /2+? ) =-Tan?
Sin (3? /2-? )=-cos？
cos(3？ /2-? ) =-sin?
Tan (3? /2-? )=cot？
cot(3？ /2-? ) = Tan?
Mathematical induction formula formula formula 1. Mathematical inductive formula memory
? Odd couples, symbols look at quadrants? .
? Odd or even? What do you mean? Parity of multiples of /2? Change and invariability? Refers to the change of the name of a trigonometric function:? Change? It refers to sine changing into cosine and tangent changing into cotangent. (and vice versa)? Symbols look at quadrants? It means: angle? As an acute angle, do not consider? The quadrant of the angle, see n? (? /2) is the quadrant angle, so we can get whether the right side of the equation is positive or negative.
2. Symbolic judgment
? One is no problem; Two sinusoids; Cut in twos and threes; Four cosines? . The meaning of this formula 12 is: What are the four trigonometric functions at any angle in the first quadrant? +? ; The second quadrant is only sine. +? , the rest are all? -? ; What are the tangents and cotangents of the third quadrant? +? , the rest are all? -? ; Only cosine in the fourth quadrant? +? , the rest are all? -? .