Tan (2kπ+α) = tan α, Cot (2kπ+α) = Cot α, where k ∈ z;

(2) sin(-α)= -sinα，cos(-α)=cosα，

tan(-α)= -tanα，cot(-α)= -cotα

(3)sin(π+α)= -sinα，cos(π+α)= -cosα，

tan(π+α)=tanα，cot(π+α)=cotα

(4)sin(π-α)=sinα，cos(π-α)= -cosα，

tan(π-α)= -tanα，cot(π-α)= -cotα

(5)sin(π/2-α)=cosα，cos(π/2-α)=sinα，

tan(π/2-α)=cotα，cot(π/2-α)=tanα

(6) sin(π/2+α)= cosα，cos(π/2+α)= -sinα，

tan(π/2+α)= -cotα，cot(π/2+α)= -tanα

(7)sin(3π/2+α)= -cosα，cos(3π/2+α)=sinα，

tan(3π/2+α)= -cotα，cot(3π/2+α)= -tanα

(8)sin(3π/2-α)= -cosα，cos(3π/2-α)= -sinα，

tan(3π/2-α)= cotα，cot(3π/2-α)= tanα

(k π/2 α), where k∈Z

Note: for the convenience of doing the problem, we used to regard α as an angle located in the first quadrant and less than 90;

When k is an odd number, the trigonometric function on the right side of the equation changes, for example, sin becomes cos. Even numbers remain unchanged;

The quadrant of the angle (k π/2 α) is used to determine the positive and negative trigonometric function on the right side of the equation.

Example: tan(3π/2 +α)= -cotα.

In this formula, k=3 is an odd number, so the strain on the right side of the equation is cot.

Moreover, the angle ∵ (3π/2 +α) is in the fourth quadrant, and tan is negative in the fourth quadrant, so in order to make the equation hold, the right side of the equation should be -cotα.

Positive and negative distribution of trigonometric function in each quadrant

Sin: the first and second quadrants are positive; The third and fourth quadrants are negative

Cos: the first quadrant and the fourth quadrant are positive; The second and third quadrants are negative.

Cot and tan: the first and third quadrants are positive; The second and fourth quadrants are negative.

If you have any other questions, please contact me. I'm happy to help you with your math problems.