Question

convert the angle $\theta = -\frac{3\pi}{4}$ to degree measurement.
(a) $-135^{\circ}$ (b) $225^{\circ}$ (c) $-150^{\circ}$ (d) $300^{\circ}$
question 4
convert the angle $\theta = \frac{5\pi}{3}$ to degree measurement.
(a) $-135^{\circ}$ (b) $225^{\circ}$ (c) $-150^{\circ}$ (d) $300^{\circ}$

Explanation:

First Question (Converting $-\frac{3\pi}{4}$ to degrees)

Step1: Recall the conversion formula

To convert radians to degrees, we use the formula: Degree = Radian $\times \frac{180^\circ}{\pi}$.

Step2: Substitute the given radian value

We have $\theta = -\frac{3\pi}{4}$. Substitute into the formula:
Degree $= -\frac{3\pi}{4} \times \frac{180^\circ}{\pi}$
The $\pi$ in the numerator and denominator cancels out:
Degree $= -\frac{3}{4} \times 180^\circ$
Calculate $-\frac{3\times180^\circ}{4} = -\frac{540^\circ}{4} = -135^\circ$

Step1: Recall the conversion formula

To convert radians to degrees, we use the formula: Degree = Radian $\times \frac{180^\circ}{\pi}$.

Step2: Substitute the given radian value

We have $\theta = \frac{5\pi}{3}$. Substitute into the formula:
Degree $= \frac{5\pi}{3} \times \frac{180^\circ}{\pi}$
The $\pi$ in the numerator and denominator cancels out:
Degree $= \frac{5}{3} \times 180^\circ$
Calculate $\frac{5\times180^\circ}{3} = 5\times60^\circ = 300^\circ$

Answer:

a. $-135^\circ$

Second Question (Converting $\frac{5\pi}{3}$ to degrees)