Explanation: for example, sin(x+k*pi/2). The so-called parity invariance means that if k is an even number, the name of the simplified trigonometric function remains unchanged (sin or sin, cos or cos, tan or tan); If k is an odd number, then after simplification, sin becomes cos, cos becomes sin, tan becomes cot, and cot becomes tan. The so-called sign quadrant is to assume that X belongs to the first quadrant (because the trigonometric functions of the first quadrant are all positive), and then rotate k*pi/2 counterclockwise to see which quadrant it falls into and whether the sign changes.

Example: cos(-pi/2-x)

Because -pi/2 and k are both odd numbers, the name of the simplified trigonometric function is sin.

Assuming that X is in the first quadrant, then -x is in the fourth quadrant, which rotates counterclockwise by -pi/2 (that is, rotates clockwise by pi/2) and then falls to the third quadrant, and the cosine cos value of the third quadrant is negative.

So the original formula =-sin(x)

2. Sine, cosine and tangent of the sum of two angles: this can only be used for backrest.

3, double angle formula: recite it, not very annoying; It can be simply deduced from the sum and difference formula of two angles.

4. Half-angle formula: because it involves the number after the root sign, try not to use it; You can also use the double angle formula to derive it, so you don't have to recite it.

5. auxiliary angle formula: A×sin(x)+B×cos(x)=C×sin(x+f)

Where c = sqrt (a 2+b 2), cos(f)=A/C, and sin (f) = b/C, notice that cos(f) is divided by the coefficient before sin and converted into the form of cos. I always change the inductive formula into SIN before using it.

6. Vector method: This method is designed for vectors that you may not have talked about. It has a limited application range, is a graphical solution, and is suitable for approximate calculation in engineering.

Scope of application: a/kloc-0 /× SIN (x+f1)+a2× sin (x+F2)+... can only be the sum of several trigonometric functions with the same name of sin or cos; The coefficients of the independent variables in trigonometric functions are the same, but the difference is only the phase difference (i.e. sine and cosine, homophone, same frequency, addition). Symbols in trigonometric functions can be solved by phase)

Methods: Let x=0, take the origin as the starting point, and make line segments (I = 1, 2, 3, ...) with the length of Ai and at right angles to the X axis. The direction of the line segment is the starting point, pointing to the end point (just like the force in physics), and then the resultant force is equivalent to the parallelogram law of forced synthesis. Then the length of the line segment representing the resultant force is c, which forms a positive angle with X-week.

7, product sum and difference and difference product: not back, on-site derivation.

(1) and differential product: such as sin (x)+sin (y) (like COS, so is subtraction). Write X as [(x+y)/2]+[(x-y)/2], and Y as [(x+y)/2]-[ (.

(2) Product sum and difference: derived from sine and cosine formulas of sum and difference of two angles.