Question

question 3
state the reference angle for the given angle.
-115°
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question 4
state the reference angle for the given angle.
-250°
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Explanation:

Step1: Find the positive coterminal angle for \(-115^{\circ}\)

Add \(360^{\circ}\) to \(-115^{\circ}\): \(-115^{\circ}+360^{\circ} = 245^{\circ}\)

Step2: Determine the reference angle for \(245^{\circ}\)

Since \(245^{\circ}\) is in the third - quadrant (\(180^{\circ}<245^{\circ}<270^{\circ}\)), the reference angle formula is \(\theta - 180^{\circ}\). So, \(245^{\circ}-180^{\circ}=65^{\circ}\)

Step3: Find the positive coterminal angle for \(-250^{\circ}\)

Add \(360^{\circ}\) to \(-250^{\circ}\): \(-250^{\circ}+360^{\circ}=110^{\circ}\)

Step4: Determine the reference angle for \(110^{\circ}\)

Since \(110^{\circ}\) is in the second - quadrant (\(90^{\circ}<110^{\circ}<180^{\circ}\)), the reference angle formula is \(180^{\circ}-\theta\). So, \(180^{\circ}-110^{\circ} = 70^{\circ}\)

Answer:

For \(-115^{\circ}\), the reference angle is \(65^{\circ}\).
For \(-250^{\circ}\), the reference angle is \(70^{\circ}\).