Given the angle shown in the following figure:
The length of the line segment from the origin to the point (4, -3) = h
[tex]h=\sqrt{(4)^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5[/tex]
So, we have the point (x,y) = (4, -3) and h = 5
We will find the six trigonometric functions of the angle as follows:
[tex]\begin{gathered} sin\theta=\frac{y}{h}=\frac{-3}{5} \\ \\ cos\theta=\frac{x}{h}=\frac{4}{5} \\ \\ tan\theta=\frac{y}{x}=\frac{-3}{4} \\ \\ sec\theta=\frac{h}{x}=\frac{5}{4} \\ \\ cosec\theta=\frac{h}{y}=\frac{5}{-3} \\ \\ cot\theta=\frac{x}{y}=\frac{4}{-3} \end{gathered}[/tex]
