Question

1. what is $85^circ$ in radians?

a. $85\pi$ radians c. $\frac{17}{36}$ radians
b. $\frac{15300}{\pi}$ radians d. $\frac{17}{36}\pi$ radians

1. what is $-240^circ$ in radians?

a. $-240\pi$ radians c. $\frac{-43200}{\pi}$ radians
b. $-\frac{4}{3}$ radians d. $-\frac{4}{3}\pi$ radians

Explanation:

Question 12

Step1: Recall the conversion formula

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

Step2: Apply the formula to \( 85^\circ \)

Substitute \( 85 \) for degrees in the formula: \( 85 \times \frac{\pi}{180} \).

Step3: Simplify the fraction

Simplify \( \frac{85}{180} \) by dividing numerator and denominator by 5: \( \frac{17}{36} \). So, \( 85^\circ = \frac{17}{36}\pi \) radians.

Step1: Recall the conversion formula

Use the formula \( \text{Radians} = \text{Degrees} \times \frac{\pi}{180} \) for converting degrees to radians.

Step2: Apply the formula to \( -240^\circ \)

Substitute \( -240 \) for degrees: \( -240 \times \frac{\pi}{180} \).

Step3: Simplify the fraction

Simplify \( \frac{-240}{180} \) by dividing numerator and denominator by 60: \( \frac{-4}{3} \). So, \( -240^\circ = -\frac{4}{3}\pi \) radians.

Answer:

D. \( \frac{17}{36}\pi \) radians

Question 13