# Thread: Converting between Radians and Degrees - help?

1. ## Converting between Radians and Degrees - help?

Hello, I'm coming here because I need help understanding a few math concepts, and this looks like a friendly community .

At the moment, I need help learning how to quickly and easily convert between radians and degrees. I am schooled over the internet, and they don't go into much detail in this section of the textbook.

The examples they give are:

Convert 300 degrees into radians.

It then shows the formula: 300 degrees = 300 degrees ((pi)radians/180 deg.)

giving the final answer of 5/3pi radians. How do I arrive at this answer?

The other example is:

Convert -3/4pi radians to degrees.

For this one the formula is not given, but they end up with -135 degrees.

Any help would be appreciated

2. Originally Posted by AlderDragon
Hello, I'm coming here because I need help understanding a few math concepts, and this looks like a friendly community .

At the moment, I need help learning how to quickly and easily convert between radians and degrees. I am schooled over the internet, and they don't go into much detail in this section of the textbook.

The examples they give are:

Convert 300 degrees into radians.

It then shows the formula: 300 degrees = 300 degrees ((pi)radians/180 deg.)
the formulas are:

$\text{degrees} \times \frac {\pi}{180} = \text{Radians}$

and

$\text{Radians} \times \frac {180}{\pi} = \text{Degrees}$

so, $300^\circ = 300 \times \frac {\pi}{180} = \frac {300 \pi}{180} = \frac {5 \pi}{3}$....by simplifying the fraction

now you try the next

3. Thanks Jhevon, that helped me. I did another one asking to convert 105 degrees into radians and I got 7pi/12. I'm pretty sure this is right.

My next problem asks me to do the opposite and convert radians into degrees.

The exact question was "Convert 7pi/5 into exact degree measure"

Using your formula, I set up the fractions:

(7pi/5)(180/pi)

Then got 1260pi/5pi

simplified to 252 degrees. Is this correct?

4. Originally Posted by AlderDragon
Thanks Jhevon, that helped me. I did another one asking to convert 105 degrees into radians and I got 7pi/12. I'm pretty sure this is right.

My next problem asks me to do the opposite and convert radians into degrees.

The exact question was "Convert 7pi/5 into exact degree measure"

Using your formula, I set up the fractions:

(7pi/5)(180/pi)

Then got 1260pi/5pi

simplified to 252 degrees. Is this correct?
yes