Question

Math

Posted 3 months ago

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

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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 $\frac{180^\circ}{\pi}$

step 2

Multiply the given angle in radians by the conversion factor: $\theta = \frac{133\pi}{72} \times \frac{180^\circ}{\pi}$

step 3

Simplify the expression by canceling $\pi$ and calculating the product: $\theta = \frac{133 \times 180^\circ}{72}$

step 4

Divide 133 by 72 and multiply by 180 to get the exact degree measure: $\theta = 332.5^\circ$

Answer

$\theta = 332.5^\circ$

Key Concept

Conversion from radians to degrees

Explanation

To convert an angle from radians to degrees, multiply by $\frac{180^\circ}{\pi}$. The exact degree measure of $\frac{133\pi}{72}$ radians is $332.5^\circ$.

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