Question

Answer the following. (a) Find an angle between 0° and 360° that is coterminal with - 58°. 16л (b) Find an angle between 0 and 2π that is coterminal with 16pie/3 Give exact values for your answers.

Answer 1

(a) Given that the angle must be coterminal with this other angle:

$-58\text{\degree}$

By definition, Coterminal Angles have the same initial side and they also have the same terminal side.

In this case, knowing that the angle must be between these angles:

$0\text{\degree and }360\text{\degree}$

You can find it by adding 360 degrees to the given angle:

$-58\text{\degree}+360\text{\degree}=302\text{\degree}$

(b) Given the angle:

$\frac{16\pi}{3}$

You know that the coterminal angle must be between:

$0\text{ and }2\pi$

Therefore, you can find it as follows:

$\frac{16\pi}{3}-2\pi=\frac{16\pi-(3)(2\pi)}{3}=\frac{10\pi}{3}$

Hence, the answers are:

(a)

$302\text{\degree}$

(b)

$\frac{10\pi}{3}\text{ }radians$