### 5Extending trigonometry to angles of any size

This chapter makes it possible for us to use trig ratios with angles of any size, and looks at the graphs of these trig functions. These are very important in many physical applications, so we look at what happens if we shift them and combine them. We also look at methods of handling trig functions and equations.

The chapter is divided into the following sections.

**5.A Giving meaning to trig functions of any size of angle**

(a) Extending sin and cos,

(b) The graph of *y* = tan *x* from 0° to 90°,

(c) Defining the sin, cos and tan of angles of any size,

(d) How does *X* move as *P* moves round its circle?

(e) The graph of tan *θ* for any value of *θ,*

(f) Can we find the angle from its sine?

(g) sin^{–1} *x* and cos