Answer: \(135^\circ\) is equivalent to \(\dfrac{3\pi}{4}\) radians.

\(300^\circ\) is equivalent to \(\dfrac{5\pi}{3}\) radians.

Solution Method: To convert from degrees to radians, we use the formula\begin{equation*}
        \text{degrees } \times \frac{\pi}{180} = \text{ radians}
 \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\\
        \frac{\pi}{180} &= 1^\circ
\end{align*}Now, to convert \(135^\circ,\)\begin{align*}
        135^\circ &= 135 \times \frac{\pi}{180} \text{ radians}\\ 
        &= \frac{135\pi}{180} \text{ radians}\\
        &= \frac{27\pi}{36} \text{ radians}\\
        &= \frac{3\pi}{4} \text{ radians}
\end{align*}And\begin{align*}
        300^\circ &= 300 \times \frac{\pi}{180} \text{ radians}\\ 
        &= \frac{300\pi}{180} \text{ radians}\\
        &= \frac{10\pi}{6} \text{ radians}\\
        &= \frac{5\pi}{3} \text{ radians}
\end{align*}

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Degree and Radian Angle Measure Exercise 1

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*}

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Degree and Radian Angle Measure Exercise 2