Chapter 8, Problem 1RE

Convert to radian measure in terms of π:

  (A) 30°    (B) 45°    (C) 60°    (D) 90°

To determine

To find: The radian measure of $30°$.

Answer to Problem 1RE

The radian measure for $30°$ is $\frac{\pi }{6}$.

Explanation of Solution

Formula used:

Degree-radian conversion:

$\frac{{\theta }_{\mathrm{deg}}}{180°}=\frac{{\theta }_{rad}}{\pi \text{ rad}}$.

Calculation:

It is given that ${\theta }_{\mathrm{deg}}=30°$.

Substitute the value of ${\theta }_{\mathrm{deg}}$ in the formula and compute the value of ${\theta }_{rad}$.

$\begin{array}{l}\frac{30°}{180°}=\frac{{\theta }_{rad}}{\pi \text{ rad}}\\ {\theta }_{rad}=\frac{30°\times \pi }{180°}\\ {\theta }_{rad}=\frac{\pi }{6}\end{array}$

Therefore, the radian measure for $30°$ is $\frac{\pi }{6}$.

To determine

To find: The radian measure of $45°$.

Answer to Problem 1RE

The radian measure for $45°$ is $\frac{\pi }{4}$.

Explanation of Solution

It is given that ${\theta }_{\mathrm{deg}}= 45°$.

Substitute the value of ${\theta }_{\mathrm{deg}}$ in the formula and compute the value of ${\theta }_{rad}$.

$\begin{array}{l}\frac{ 45°}{180°}=\frac{{\theta }_{rad}}{\pi \text{ rad}}\\ {\theta }_{rad}=\frac{ 45°\times \pi }{180°}\\ {\theta }_{rad}=\frac{\pi }{4}\end{array}$

Therefore, the radian measure for $45°$ is $\frac{\pi }{4}$.

To determine

To find: The radian measure of $60°$.

Answer to Problem 1RE

The radian measure for $60°$ is $\frac{\pi }{3}$.

Explanation of Solution

It is given that ${\theta }_{\mathrm{deg}}=60°$.

Substitute the value of ${\theta }_{\mathrm{deg}}$ in the formula and compute the value of ${\theta }_{rad}$.

$\begin{array}{l}\frac{60°}{180°}=\frac{{\theta }_{rad}}{\pi \text{ rad}}\\ {\theta }_{rad}=\frac{60°\times \pi }{180°}\\ {\theta }_{rad}=\frac{\pi }{3}\end{array}$

Therefore, the radian measure for ${60}^{\text{o}}$ is $\frac{\pi }{3}$.

To determine

To find: The radian measure of $90°$.

Answer to Problem 1RE

The radian measure for $90°$ is $\frac{\pi }{2}$.

Explanation of Solution

It is given that ${\theta }_{\mathrm{deg}}=90°$.

Substitute the value of ${\theta }_{\mathrm{deg}}$ in the formula and compute the value of ${\theta }_{rad}$.

$\begin{array}{l}\frac{90°}{180°}=\frac{{\theta }_{rad}}{\pi \text{ rad}}\\ {\theta }_{rad}=\frac{90°\times \pi }{180°}\\ {\theta }_{rad}=\frac{\pi }{2}\end{array}$

Therefore, the radian measure for $90°$ is $\frac{\pi }{2}$.