Question

convert angle $\theta = 225^{\circ}$ to its radian measurement.\
(a) $\frac{5\pi}{3}$ (b) $\frac{4\pi}{3}$ (c) $\frac{5\pi}{4}$ (d) $\frac{5\pi}{6}$\
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question 2\
convert the angle $\theta = -150^{\circ}$ to radian measurement.\
(a) $\frac{5\pi}{3}$ (b) $-\frac{3\pi}{4}$ (c) $\frac{5\pi}{4}$ (d) $-\frac{5\pi}{6}$

Explanation:

Question 1:

Step1: Recall degree to radian formula

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

Step2: Apply the formula to \( 225^\circ \)

Substitute \( \text{Degree} = 225 \) into the formula:
\( 225 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{225}{180} \). Both numerator and denominator are divisible by 45:
\( \frac{225 \div 45}{180 \div 45} = \frac{5}{4} \)
So, \( 225^\circ = \frac{5\pi}{4} \)

Step1: Recall degree to radian formula

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

Step2: Apply the formula to \( -150^\circ \)

Substitute \( \text{Degree} = -150 \) into the formula:
\( -150 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{-150}{180} \). Both numerator and denominator are divisible by 30:
\( \frac{-150 \div 30}{180 \div 30} = \frac{-5}{6} \)
So, \( -150^\circ = -\frac{5\pi}{6} \)

Answer:

c. \( \frac{5\pi}{4} \)

Question 2: