Question

converting from degrees to radians in exercises 35 and 36, convert each degree measure to radian measure as a multiple of π. do not use a calculator
35.
a. 120°
b. -20°
36.
a. -60°
b. 144°

Explanation:

35a. Converting \( 120^\circ \) to radians

Step1: Recall the conversion formula

To convert degrees to radians, we use the formula: \( \text{Radian measure} = \text{Degree measure} \times \frac{\pi}{180} \)

Step2: Substitute the degree measure

Substitute \( 120^\circ \) into the formula: \( 120 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{120}{180} \) by dividing numerator and denominator by 60: \( \frac{120\div60}{180\div60} = \frac{2}{3} \)
So, \( 120^\circ = \frac{2\pi}{3} \) radians.

Step1: Recall the conversion formula

Use the formula \( \text{Radian measure} = \text{Degree measure} \times \frac{\pi}{180} \)

Step2: Substitute the degree measure

Substitute \( -20^\circ \) into the formula: \( -20 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{-20}{180} \) by dividing numerator and denominator by 20: \( \frac{-20\div20}{180\div20} = \frac{-1}{9} \)
So, \( -20^\circ = -\frac{\pi}{9} \) radians.

Step1: Recall the conversion formula

Use \( \text{Radian measure} = \text{Degree measure} \times \frac{\pi}{180} \)

Step2: Substitute the degree measure

Substitute \( -60^\circ \) into the formula: \( -60 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{-60}{180} \) by dividing numerator and denominator by 60: \( \frac{-60\div60}{180\div60} = \frac{-1}{3} \)
So, \( -60^\circ = -\frac{\pi}{3} \) radians.

Answer:

\( \frac{2\pi}{3} \)

35b. Converting \( -20^\circ \) to radians