# Precalculus converting radians to degrees.

I'm studying for a precalc test and I've kind of hit a brick wall with conversion. I've searched for help but only found things on converting from pi radians.

I found some questions that consist of things like converting 7.58 rad to degree.

How do I do this, what is this type of conversion even called?

Whenever converting from one quantity to another, always remember to multiply by $1$.

We know that $2\pi\mathrm{~rad}=360^\circ$. This can be also be written as $\frac{2\pi\mathrm{~rad}}{360^\circ}=1$ or as $1=\frac{360^\circ}{2\pi\mathrm{~rad}}$.

If you want to convert, say, $7.58$ rad to degrees, just multiply by the $1$ that has rad in the denominator so that it cancels out and you get the units that you want (degrees).

$$\require{cancel}7.58\cancel{\mathrm{~rad}}\times\frac{360^\circ}{2\pi\cancel{\mathrm{~rad}}}\approx 434.3^\circ$$

If you want to convert, say, $200^\circ$ to radians, just multiply by the $1$ that has degrees in the denominator so that it cancels out and you get the units that you want (radians).

$$200\cancel{^\circ}\times\frac{2\pi\mathrm{~rad}}{360\cancel{^\circ}}\approx 3.49\mathrm{~rad}$$

• Do you mind me asking how you did the math for that conversion? I'm still kind of confused. – Alex Apr 8 '14 at 4:15
• For the first example, I used a calculator: $7.58\times 360\div (2\times\pi)=$, where $\pi$ is a button on the calculator. A simpler way would be to use $7.58\times 180\div\pi=$. – Joel Reyes Noche Apr 8 '14 at 4:17
• I'll upvote when I have the reputation, thanks! – Alex Apr 8 '14 at 4:21

$$\theta_{\text{rad}}=\theta^\circ\times\dfrac{\pi}{180^\circ}\text{ rad}$$ I believe it's called "degrees to radians".

• @JoelReyesNoche Yes, thanks! – user122283 Apr 8 '14 at 4:12