Question

chapter ii.8
score: 1/6 answered: 2/6
question 3
convert the radian measure of the angle $\theta$ into degree measure of the angle: $\theta=\frac{262}{272}pi$.

Explanation:

Step1: Recall conversion formula

To convert radians to degrees, use the formula $D = R\times\frac{180^{\circ}}{\pi}$, where $D$ is the degree - measure and $R$ is the radian - measure.

Step2: Substitute the given radian value

Given $R=\frac{262}{272}\pi$. Substitute it into the formula: $D=\frac{262}{272}\pi\times\frac{180^{\circ}}{\pi}$.

Step3: Simplify the expression

The $\pi$ terms cancel out. Then $D = \frac{262\times180}{272}$. Calculate $262\times180 = 47160$ and $47160\div272=\frac{47160}{272}=\frac{11790}{68}=\frac{5895}{34}\approx173.38^{\circ}$.

Answer:

$\frac{5895}{34}\text{ degrees}$ (or approximately $173.38^{\circ}$)