# Trigonometric functions of negative angles

**Trigonometric functions of negative angles**:

let and be any two angles equal in magnitude but opposite in sign.

If we place each of them in the standard position it can be observed that the two angles are symmetrically placed on either side of x-axis.

Suppose we construct a circle of radius “r” with centre “o” , it will cut the terminal arms of angles and

as shown in figure below:

Let thee points “P” and “P’” respectively. Clearly , the abscissa of P is the same as that of P’ , both in magnitude and

direction. But the ordinates of P and P’ are equal in magnitude but opposite in sign. If we denote the point

P by P(x,y) , then the point P’ will have the co-ordinates P’(x,-y), thus we have:

And:

Similarly:

and

Thus:

and

Related posts:

- Derivatives of Trigonometric functions. As you know, The functions SINE x(sin x) , CO-SECANT...
- Derivatives of inverse trigonometric functions Inverse trigonometric functions are the inverse of trigonometric functions ....
- Pythagorian Identities Fundamental Pythagorian identity of trigonometry and other basic trigonometric formulas...
- Trigonometric Functions What are trigonometric functions such as sine , cosine ,...
- Properties of trigonometric functions Properties or sine , cosine , tangent , cosine ,...