Question

Determine the angle between 0 and 2π that is coterminal to 1020°.

Answer 1

We will have the following:

First, we know that a whole rotation is 360°, so we can see that the number of rotations that are take are 2:

$\begin{cases}360\cdot2=720 \\ \\ 360\cdot3=1080\end{cases}$

So, we find the remaining angle:

$1020-720=300$

So, we transform that to radians:

$300\cdot\frac{\pi}{180}=\frac{5}{3}\pi$

So, the coterminal angle to 1020° is 300° which in radians is:

$\frac{5\pi}{3}$