Questions: Determine the reference angle, in radians, associated with the given angle. Write the exact answer. Do not round. θ = 15π/16

Determine the reference angle, in radians, associated with the given angle. Write the exact answer. Do not round. θ = 15π/16
Transcript text: Determine the reference angle, in radians, associated with the given angle. Write the exact answer. Do not round. \[ \theta=\frac{15 \pi}{16} \]
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Solution

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Solution Steps

Step 1: Identify the Given Angle

The given angle is \(\theta = \frac{15\pi}{16}\).

Step 2: Determine the Reference Angle

To find the reference angle for an angle \(\theta\) that is more than \(\pi\) but less than \(2\pi\), use the formula: \[ \text{Reference Angle} = 2\pi - \theta \]

Step 3: Calculate the Reference Angle

Substitute \(\theta = \frac{15\pi}{16}\) into the formula: \[ \text{Reference Angle} = 2\pi - \frac{15\pi}{16} = \frac{32\pi}{16} - \frac{15\pi}{16} = \frac{17\pi}{16} \]

Final Answer

The reference angle is \(\boxed{\frac{17\pi}{16}}\).

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