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Question
Math
Posted 3 months ago

Convert the angle θ=133π72\theta=\frac{133 \pi}{72} radians to degrees.
Express your answer exactly.
θ=
\theta=

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Answer from Sia
Posted 3 months ago
Solution by Steps
step 1
To convert radians to degrees, we use the conversion factor 180π\frac{180^\circ}{\pi}
step 2
Multiply the given angle in radians by the conversion factor: θ=133π72×180π\theta = \frac{133\pi}{72} \times \frac{180^\circ}{\pi}
step 3
Simplify the expression by canceling π\pi and calculating the product: θ=133×18072\theta = \frac{133 \times 180^\circ}{72}
step 4
Divide 133 by 72 and multiply by 180 to get the exact degree measure: θ=332.5\theta = 332.5^\circ
Answer
θ=332.5\theta = 332.5^\circ
Key Concept
Conversion from radians to degrees
Explanation
To convert an angle from radians to degrees, multiply by 180π\frac{180^\circ}{\pi}. The exact degree measure of 133π72\frac{133\pi}{72} radians is 332.5332.5^\circ.

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