Question

convert the angle θ = \\(\frac{9\pi}{5}\\) radians to degrees. express your answer exactly. θ = \\(\square\\)° show calculator

Explanation:

Step1: Recall the conversion formula

To convert radians to degrees, we use the formula: \( \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} \)

Step2: Substitute the given radian measure

We are given \( \theta = \frac{9\pi}{5} \) radians. Substitute this into the formula:
\( \theta = \frac{9\pi}{5} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) in the numerator and denominator cancels out:
\( \theta = \frac{9}{5} \times 180^\circ \)
Calculate \( \frac{9 \times 180^\circ}{5} \):
First, divide 180 by 5: \( 180 \div 5 = 36 \)
Then multiply by 9: \( 9 \times 36^\circ = 324^\circ \)

Answer:

\( 324 \)