Question

The measure of two angles in standard position is given. Determine whether the angles are coterminal

$\frac{32\pi }{3},\frac{11\pi }{3}$

Short answer

No, the angles are not coterminal.

Step-by-step solution

Step 1. Given information.

The given angles are:

$\frac{32\pi }{3},\frac{11\pi }{3}$.

Step 2. Explanation.

Two angles in standard position are coterminal if their sides coincide.

We subtract given angles to find out the difference between these angles.

Now if the resulting difference is any multiple of $2\pi$ then they are coterminal angles.

Step 3. Calculation.

First, subtract these given angles, we get:

$\frac{32\pi }{3}-\frac{11\pi }{3}=\frac{21\pi }{3}=7\pi$

Now find out if the resulting angle is multiple of $2\pi$, by dividing it by $2\pi$, we get:

$\frac{7\pi }{2\pi }=3.5$

We see that the difference between these angles is not multiple of $2\pi$ so these angles are not coterminal.