Question

draw the terminal side of 135° 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 positive angle that is coterminal.
find a negative angle that is coterminal.

Explanation:

Step1: Understand coterminal angles

Coterminal angles are angles that have the same terminal side. The formula for finding coterminal angles is \(\theta\pm360^{\circ}n\), where \(n\) is an integer.

Step2: Find a positive coterminal angle

For a positive coterminal angle with \(135^{\circ}\), let \(n = 1\). Then \(\theta+360^{\circ}n=135^{\circ}+ 360^{\circ}=495^{\circ}\)

Step3: Find a negative coterminal angle

For a negative coterminal angle with \(135^{\circ}\), let \(n = 1\). Then \(\theta - 360^{\circ}n=135^{\circ}-360^{\circ}=-225^{\circ}\)

Answer:

Positive coterminal angle: \(495^{\circ}\)
Negative coterminal angle: \(-225^{\circ}\)