Question

find the measure of an angle with measure between 0° and 360° that is coterminal with an angle measuring -800°. find the measure of an angle with measure between 0° and 360° that is coterminal with an angle measuring 800°.

Explanation:

Step1: Find coterminal angle for \(-800^{\circ}\)

Coterminal angles are found by adding \(360^{\circ}n\) (\(n\) is an integer). For \(-800^{\circ}\), we want \(0^{\circ}<\theta < 360^{\circ}\).
Let's find \(n\) such that \(\theta=-800 + 360n\).
If \(n = 3\), then \(\theta=-800+360\times3=-800 + 1080\)

$$ \theta=-800 + 1080=280^{\circ} $$

Step2: Find coterminal angle for \(800^{\circ}\)

Let \(\theta = 800-360n\), \(0^{\circ}<\theta<360^{\circ}\).
If \(n = 2\), then \(\theta=800-360\times2=800 - 720\)

$$ \theta=80^{\circ} $$

Answer:

For \(-800^{\circ}\): \(280^{\circ}\)
For \(800^{\circ}\): \(80^{\circ}\)