Question

Find a positive angle less than one revolution around the unit circle that is co-terminal with the given angle: 52pi/5

Answer 1

72°

Explanation:

Given angle =
`(52\pi)/(5)`

we know,
`\pi=180^\circ`

so, given angle =
`(52)/(5) * 180 = 1872^\circ`

Also, one complete revolution = 360°

we can write the given angle as

1872° = 5 x 360° + 72°

So, the given angle is the sum of five complete revolutions (1800°) and 72°

Therefore, positive angle less than one revolution around the unit circle that is co-terminal with the given angle is 72°.

Answer 2

we know that
Two angles are said to be co-terminal if they have the same initial side and
the same terminal side.

(52π/5)-----> 10.4π
so
(52π/5)-5*2π------> (2π/5)

the answer is
the positive angle less than one revolution around the unit circle that is co-terminal with angle of 52π/5 is 2π/5