Question

use the fact that there are 2pi radians in each circle to find another angle,smaller than 2pi,that is equivalent to 13pi/4

Answer 1

`\frac{13\pi}4\equiv\frac\pi4\mod2\pi`

Or, put another way, since
`\frac{13\pi}4=2\pi+\frac\pi4`, it follows that
`\frac\pi4` is an equivalent angle.

Answer 2

Explanation:

Given is an angle
`(13\pi)/(4)`

We know that there are 2pi radians in each circle

Hence after crossing 2pi radians, the values repeat

`(13\pi)/(4)=2\pi+(5\pi)/(4)`

Hence equivalent angle is

`(5\pi)/(4)`

i.e. in the III quadrant making pi/4 with negative x axis.