Question

draw the terminal side of $-45^{circ}$ in standard position. hint: plot the starting point at the origin, and then plot a point on the terminal side of the angle. find a nonnegative angle that is coterminal. find a negative angle that is coterminal. question help: video ebook message instructor submit question

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles are given by the formula \(\theta + n\times360^{\circ}\), where \(n\in\mathbb{Z}\) ( \(n\) is an integer).

Step2: Find a non - negative coterminal angle

Let \(n = 1\). For \(\theta=-45^{\circ}\), we use the formula \(\theta + n\times360^{\circ}\).
Substitute \(\theta=-45^{\circ}\) and \(n = 1\) into the formula: \(-45^{\circ}+1\times360^{\circ}=315^{\circ}\)

Step3: Find a negative coterminal angle

Let \(n=-1\). Substitute \(\theta=-45^{\circ}\) and \(n=-1\) into the formula \(\theta + n\times360^{\circ}\)
\(-45^{\circ}+(- 1)\times360^{\circ}=-405^{\circ}\)

Answer:

Non - negative coterminal angle: \(315^{\circ}\)
Negative coterminal angle: \(-405^{\circ}\)