Degree and Radian Angle Measure Exercise 2
Author: Hannah Solomon
The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Reveal Answer" to see the answer to the problem.
Exercises
Answer: \(\dfrac{\pi}{3}\) radians is equivalent to \(60^\circ\)
\(\dfrac{7\pi}{4}\) radians is equivalent to \(315^\circ\)
Solution Method: To convert from radians to degrees we use the formula \begin{equation*}
\text{radians } \times \frac{180}{\pi} = \text{ degrees}
\end{equation*}This conversion factor comes from the fact that \begin{equation*}
2\pi \text{ radians} = 360^\circ
\end{equation*}Then we have\begin{align*}
\pi \text{ radians} &= 180^\circ\\
1 \text{ radian} &= \frac{180^\circ}{\pi}
\end{align*}So we have \begin{align*}
\frac{\pi}{3} \text{ radians} &= \frac{\pi}{3} \times \frac{180}{\pi} \text{ degrees}\\
&= \frac{180}{3} \text{ degrees} \\
&= 60 ^\circ
\end{align*}And\begin{align*}
\frac{7\pi}{4} \text{ radians} &= \frac{7\pi}{4} \times \frac{180}{\pi} \text{ degrees}\\
&= \frac{7(180)}{4} \text{ degrees} \\
&= 7(45)^\circ \\
&= 315^\circ
\end{align*}
\(\dfrac{7\pi}{4}\) radians is equivalent to \(315^\circ\)
Solution Method: To convert from radians to degrees we use the formula \begin{equation*}
\text{radians } \times \frac{180}{\pi} = \text{ degrees}
\end{equation*}This conversion factor comes from the fact that \begin{equation*}
2\pi \text{ radians} = 360^\circ
\end{equation*}Then we have\begin{align*}
\pi \text{ radians} &= 180^\circ\\
1 \text{ radian} &= \frac{180^\circ}{\pi}
\end{align*}So we have \begin{align*}
\frac{\pi}{3} \text{ radians} &= \frac{\pi}{3} \times \frac{180}{\pi} \text{ degrees}\\
&= \frac{180}{3} \text{ degrees} \\
&= 60 ^\circ
\end{align*}And\begin{align*}
\frac{7\pi}{4} \text{ radians} &= \frac{7\pi}{4} \times \frac{180}{\pi} \text{ degrees}\\
&= \frac{7(180)}{4} \text{ degrees} \\
&= 7(45)^\circ \\
&= 315^\circ
\end{align*}
