Question

2.) θ=60° 4.) θ=11π/6 θ=__(radians) θ=(radians) θ=° θ=__°

Explanation:

Step1: Find the reference angle for \(\theta = 60^{\circ}\)

The reference angle \(\theta'\) for an angle in standard position is the acute angle it makes with the \(x -\)axis. For \(\theta=60^{\circ}\), since \(60^{\circ}\) is in the first - quadrant (assuming the terminal side is in the first - quadrant as per the general problem setup for positive angles in standard position), the reference angle \(\theta'=60^{\circ}\).
To convert degrees to radians, use the formula \(x^{\circ}=x\times\frac{\pi}{180}\) radians. So, \(60^{\circ}=60\times\frac{\pi}{180}=\frac{\pi}{3}\) radians.

Step2: Find the reference angle for \(\theta=\frac{11\pi}{6}\)

The angle \(\theta = \frac{11\pi}{6}\) is in the fourth - quadrant. The formula for the reference angle \(\theta'\) of an angle \(\theta\) in the fourth - quadrant is \(\theta' = 2\pi-\theta\).

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To convert \(\frac{\pi}{6}\) radians to degrees, use the formula \(x\) radians \(=x\times\frac{180}{\pi}\) degrees. So, \(\frac{\pi}{6}\times\frac{180}{\pi}=30^{\circ}\)

Answer:

For \(\theta = 60^{\circ}\): \(\theta'=\frac{\pi}{3}\) radians and \(\theta' = 60^{\circ}\)

For \(\theta=\frac{11\pi}{6}\): \(\theta'=\frac{\pi}{6}\) radians and \(\theta' = 30^{\circ}\)