Questions: Determine two other, different positive angles that are coterminal with the angle ( phi=frac7 pi10 )

Determine two other, different positive angles that are coterminal with the angle ( phi=frac7 pi10 )
Transcript text: Determine two other, different positive angles that are coterminal with the angle \[ \phi=\frac{7 \pi}{10} \]
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Solution

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Solution Steps

Step 1: Determine the Given Angle

The given angle is \[ \phi = \frac{7\pi}{10}. \]

Step 2: Calculate the First Coterminal Angle

To find the first coterminal angle, we add \(2\pi\) to the given angle: \[ \text{coterminal angle}_1 = \phi + 2\pi = \frac{7\pi}{10} + 2\pi = \frac{7\pi}{10} + \frac{20\pi}{10} = \frac{27\pi}{10}. \]

Step 3: Calculate the Second Coterminal Angle

To find the second coterminal angle, we add \(4\pi\) to the given angle: \[ \text{coterminal angle}_2 = \phi + 4\pi = \frac{7\pi}{10} + 4\pi = \frac{7\pi}{10} + \frac{40\pi}{10} = \frac{47\pi}{10}. \]

Summary of Coterminal Angles

The two different positive angles that are coterminal with \(\phi = \frac{7\pi}{10}\) are \[ \frac{27\pi}{10} \quad \text{and} \quad \frac{47\pi}{10}. \]

Final Answer

The two different positive angles that are coterminal with \(\phi = \frac{7\pi}{10}\) are \( \boxed{\frac{27\pi}{10}} \) and \( \boxed{\frac{47\pi}{10}} \).

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