Question

which of the following angles is not coterminal with the other three?
215°
35°
-145°
575°
15 multiple choice 1 point
find the measure of an angle between 0° and 360° coterminal with an angle of -119° in standard position.
29°
61°
241°
119°

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles are of the form \(\theta + 360^{\circ}n\), where \(n\in\mathbb{Z}\) ( \(n\) is an integer).

Step2: Check each angle for the first question

• For \(215^{\circ}\):
• Let's check if it can be related to other angles.
• For \(- 145^{\circ}\), \(215^{\circ}-(-145^{\circ})=360^{\circ}\) (using \(n = 1\) in the formula \(\theta_1=\theta_2+360^{\circ}n\), here \(\theta_1 = 215^{\circ}\), \(\theta_2=-145^{\circ}\)).
• For \(575^{\circ}\), \(575^{\circ}-215^{\circ}=360^{\circ}\) (using \(n = 1\) in the formula \(\theta_1=\theta_2+360^{\circ}n\), here \(\theta_1 = 575^{\circ}\), \(\theta_2 = 215^{\circ}\)).
• \(35^{\circ}\) cannot be written as \(215^{\circ}+360^{\circ}n\) or \(-145^{\circ}+360^{\circ}n\) or \(575^{\circ}+360^{\circ}n\) for any integer \(n\).

Step3: Solve the second - question

To find a coterminal angle of \(-119^{\circ}\) between \(0^{\circ}\) and \(360^{\circ}\), we use the formula \(\alpha=-119^{\circ}+360^{\circ}n\).
Let \(n = 1\), then \(\alpha=-119^{\circ}+360^{\circ}=241^{\circ}\)

Answer:

For the first question: \(35^{\circ}\) is not coterminal with the other three.
For the second question: \(241^{\circ}\)