Question

in degree measure, the angles $\frac{pi}{3}$, $\frac{pi}{4}$, and $\frac{pi}{2}$ are respectively:
a. $30^circ, 45^circ, 90^circ$
b. $60^circ, 45^circ, 90^circ$
c. $60^circ, 30^circ, 90^circ$
d. $45^circ, 60^circ, 90^circ$

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: Convert \( \frac{\pi}{3} \) to degrees

Substitute \( \text{Radians} = \frac{\pi}{3} \) into the formula:
\( \frac{\pi}{3} \times \frac{180^\circ}{\pi} = 60^\circ \).

Step3: Convert \( \frac{\pi}{4} \) to degrees

Substitute \( \text{Radians} = \frac{\pi}{4} \) into the formula:
\( \frac{\pi}{4} \times \frac{180^\circ}{\pi} = 45^\circ \).

Step4: Convert \( \frac{\pi}{2} \) to degrees

Substitute \( \text{Radians} = \frac{\pi}{2} \) into the formula:
\( \frac{\pi}{2} \times \frac{180^\circ}{\pi} = 90^\circ \).

Answer:

B. \( 60^\circ, 45^\circ, 90^\circ \)