One whole unit circle has an angle of 2π. So, if our angle is 5π, this would be two revolutions and a half. This means that the terminal ray of this angle lies in Quadrant II at the x-axis.
The angle has an x-value of -1, a y-value of 0, and an r-value of 1.
So, the value of the six trigonometric functions are:
[tex]sin5\pi=\frac{y}{r}\Rightarrow sin5\pi=\frac{0}{1}\Rightarrow sin5\pi=0[/tex][tex]cos5\pi=\frac{x}{r}\Rightarrow cos5\pi=\frac{-1}{1}\Rightarrow cos5\pi=-1[/tex][tex]tan5\pi=\frac{y}{x}\Rightarrow tan5\pi=\frac{0}{-1}\Rightarrow tan5\pi=0[/tex][tex]csc5\pi=\frac{r}{y}\Rightarrow csc5\pi=\frac{1}{0}\Rightarrow csc5\pi=undefined[/tex][tex]sec5\pi=\frac{r}{x}\Rightarrow sec5\pi=\frac{1}{-1}\Rightarrow sec5\pi=-1[/tex][tex]cot5\pi=\frac{x}{y}\Rightarrow cot5\pi=\frac{-1}{0}\Rightarrow cot5\pi=undefined[/tex]
