Question

Math

Posted 5 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 5 months ago

Solution by Steps

step 1

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

step 2

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

step 3

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

step 4

Cancel the $\pi$ in the numerator and denominator and simplify the fraction: $\frac{133 \times 180^\circ}{72} = \frac{133 \times 5^\circ}{2} = 332.5^\circ$

step 5

Express the decimal in degrees and minutes: $332.5^\circ = 332^\circ + 0.5 \times 60' = 332^\circ 30'$

[1] Answer

$332^\circ 30'$

Key Concept

Conversion from radians to degrees

Explanation

To convert an angle from radians to degrees, multiply the radian measure by $\frac{180^\circ}{\pi}$. After multiplying, simplify the expression to get the degree measure, and if needed, convert the decimal part to minutes.

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