# What is 450 degrees in terms of radians?

Mar 21, 2018

${450}^{\circ}$ is $\frac{5 \pi}{2}$ radians.

#### Explanation:

To convert from degrees to radians, multiply by the conversion factor $\frac{\pi \quad \mathcal{r a \mathrm{di} a n s}}{180} ^ \circ$.

Here's the expression:

$\textcolor{w h i t e}{=} {450}^{\circ}$

$= {450}^{\circ} \textcolor{b l u e}{\cdot \frac{\pi \quad \mathcal{r a \mathrm{di} a n s}}{180} ^ \circ}$

$= {450}^{\textcolor{red}{\cancel{\textcolor{b l u e}{\circ}}}} \textcolor{b l u e}{\cdot \frac{\pi \quad \mathcal{r a \mathrm{di} a n s}}{180} ^ \textcolor{red}{\cancel{\textcolor{b l u e}{\circ}}}}$

$= 450 \textcolor{b l u e}{\cdot \frac{\pi \quad \mathcal{r a \mathrm{di} a n s}}{180}}$

$= \frac{450 \cdot \pi \quad \mathcal{r a \mathrm{di} a n s}}{180}$

$= \frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{450}}}}^{5} \cdot \pi \quad \mathcal{r a \mathrm{di} a n s}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{180}}}} ^ 2$

$= \frac{5 \cdot \pi \quad \mathcal{r a \mathrm{di} a n s}}{2}$

$= \frac{5 \pi \quad \mathcal{r a \mathrm{di} a n s}}{2}$

Usually written as:

$= \frac{5 \pi}{2} \quad \mathcal{r a \mathrm{di} a n s}$

That's the conversion. Hope this helped!