Question

Math

Posted 6 months ago

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

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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

To convert radians to degrees, multiply by $\frac{180}{\pi}$

step 2

Multiply $\frac{133\pi}{72}$ by $\frac{180}{\pi}$ to convert to degrees

step 3

Simplify the expression: $\frac{133\pi}{72} \times \frac{180}{\pi} = \frac{133 \times 180}{72}$

step 4

Calculate the simplified expression: $\frac{133 \times 180}{72} = 332.5$ degrees

step 5

Since we need an exact answer, express $332.5$ degrees as $332$ degrees and $30$ arcminutes

[1] Answer

$\theta = 332$ degrees $30$ arcminutes

Key Concept

Conversion from radians to degrees

Explanation

To convert an angle from radians to degrees, multiply the radian measure by $\frac{180}{\pi}$. The result can be expressed in degrees and arcminutes for an exact representation.

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