Question

Use the unit circle to evaluate the six trigonometric functions of theta
`5\pi`

Answer 1

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:

`sin5\pi=(y)/(r)\Rightarrow sin5\pi=(0)/(1)\Rightarrow sin5\pi=0`
`cos5\pi=(x)/(r)\Rightarrow cos5\pi=(-1)/(1)\Rightarrow cos5\pi=-1`
`tan5\pi=(y)/(x)\Rightarrow tan5\pi=(0)/(-1)\Rightarrow tan5\pi=0`

`sec5\pi=(r)/(x)\Rightarrow sec5\pi=(1)/(-1)\Rightarrow sec5\pi=-1`