Question

question 5
state the reference angle for the given angle.
310°
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question 6
state the reference angle for the given angle.
200°
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Explanation:

Step1: Determine the quadrant of \(310^{\circ}\)

Since \(270^{\circ}<310^{\circ}<360^{\circ}\), \(310^{\circ}\) is in the fourth quadrant.

Step2: Calculate the reference angle for \(310^{\circ}\)

The formula for the reference angle \(\theta_{r}\) of an angle \(\theta\) in the fourth quadrant is \(\theta_{r} = 360^{\circ}-\theta\).
So, \(\theta_{r}=360^{\circ} - 310^{\circ}=50^{\circ}\)

Step3: Determine the quadrant of \(200^{\circ}\)

Since \(180^{\circ}<200^{\circ}<270^{\circ}\), \(200^{\circ}\) is in the third quadrant.

Step4: Calculate the reference angle for \(200^{\circ}\)

The formula for the reference angle \(\theta_{r}\) of an angle \(\theta\) in the third quadrant is \(\theta_{r}=\theta - 180^{\circ}\)
So, \(\theta_{r}=200^{\circ}-180^{\circ} = 20^{\circ}\)

Answer:

For \(310^{\circ}\), the reference angle is \(50^{\circ}\).
For \(200^{\circ}\), the reference angle is \(20^{\circ}\).