Question

15 multiple choice 1 point
find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
\\( \frac { 4 \pi } { 3 } \\)
\\( \frac { 2 \pi } { 3 } ; - \frac { 10 \pi } { 3 } \\)
\\( \frac { 10 \pi } { 3 } ; - \frac { 2 \pi } { 3 } \\)
\\( \frac { 7 \pi } { 3 } ; - \frac { 7 \pi } { 3 } \\)
\\( \frac { 7 \pi } { 3 } ; - \frac { 2 \pi } { 3 } \\)
16 multiple choice 1 point
find the measures of two angles, one positive and one negative, that are coterminal with the given angle.

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles are given by \(\theta + 2k\pi\), where \(k\in\mathbb{Z}\). For \(\theta=\frac{4\pi}{3}\), when \(k = 1\):

$$ \frac{4\pi}{3}+2\pi=\frac{4\pi + 6\pi}{3}=\frac{10\pi}{3} $$

Step2: When \(k=-1\)

$$ \frac{4\pi}{3}-2\pi=\frac{4\pi-6\pi}{3}=-\frac{2\pi}{3} $$

Answer:

B. \(\frac{10\pi}{3};-\frac{2\pi}{3}\)