Recall that there are 360 degrees in a circle which is equivalent to \(\displaystyle 2\pi\) radians. In order to convert between radians and degrees use the relationship that, \(\displaystyle 360^\circ=2\pi \Rightarrow 180^\circ=\pi\).

Therefore, in order to convert from radians to degrees you need to multiply by \(\displaystyle \frac{180}{\pi}\). So in this particular case, 

\(\displaystyle 7\pi*\frac{180}{\pi}=1260^{\circ}\).

Recall that there are 360 degrees in a circle which is equivalent to \(\displaystyle 2\pi\) radians. In order to convert between radians and degrees use the relationship that, \(\displaystyle 360^\circ=2\pi \Rightarrow 180^\circ=\pi\).

Therefore, in order to convert from radians to degrees you need to multiply by \(\displaystyle \frac{180}{\pi}\). So in this particular case, 

\(\displaystyle \frac{4\pi}{3}*\frac{180}{\pi}=240^{\circ}\).

Recall that there are 360 degrees in a circle which is equivalent to \(\displaystyle 2\pi\) radians. In order to convert between radians and degrees use the relationship that, \(\displaystyle 360^\circ=2\pi \Rightarrow 180^\circ=\pi\).

Therefore, in order to convert from radians to degrees you need to multiply by \(\displaystyle \frac{180}{\pi}\).  So in this particular case, 

\(\displaystyle \frac{9\pi}{5}*\frac{180}{\pi}=324^{\circ}\).

Recall that there are 360 degrees in a circle which is equivalent to \(\displaystyle 2\pi\) radians. In order to convert between radians and degrees use the relationship that, \(\displaystyle 360^\circ=2\pi \Rightarrow 180^\circ=\pi\).

Therefore, in order to convert from radians to degrees you need to multiply by \(\displaystyle \frac{180}{\pi}\). So in this particular case, 

\(\displaystyle -\frac{\pi}{3}*\frac{180}{\pi}=-60^{\circ}\).

Step 1: Recall the formula to change a degree measure into radians:

The formula is: \(\displaystyle Degree\cdot \frac {\pi}{180}\).

Step 2: Plug in the angle:

\(\displaystyle 75 \cdot \frac {\pi}{180}\)

Step 3: Simplify:

We will use the \(\displaystyle 75\) and try to reduce the \(\displaystyle 180\) as much as possible. 

After Dividing by 3:

\(\displaystyle 25 \cdot \frac {\pi}{60}\)

After dividing by 5:

\(\displaystyle 5 \cdot \frac {\pi}{12}=\frac {5\pi}{12}\)


\(\displaystyle 75^\circ\) is \(\displaystyle \frac {5\pi}{12}\) in radians.

Step 1: To convert radians back to degrees, multiply that radian measure by \(\displaystyle \frac {180}{\pi}\)

Step 2: Multiply:

\(\displaystyle \frac {4\pi}{3}\cdot \frac {180}{\pi}\)

Step 3: Reduce.. The \(\displaystyle \pi\) will cancel...

\(\displaystyle \frac {4}{3} \cdot 180\)

Step 4: Divide \(\displaystyle 180\) by \(\displaystyle 3\)..

\(\displaystyle 4\cdot 60^\circ=240^\circ\)

\(\displaystyle \frac {4\pi}{3}\) is equivalent to \(\displaystyle 240^\circ\)

We know that:

\(\displaystyle 360^{\circ}=2\pi\) Radians

since the giving angle was in degrees then we multiply

\(\displaystyle 107^{\circ}*\frac{\pi}{180^{\circ}}= 1.868\)

We know that:

\(\displaystyle 360^{\circ}=2\pi\) Radians

since the giving angle was in degrees then we multiply

\(\displaystyle 45^{\circ}*\frac{\pi}{180^{\circ}}= \frac{\pi}{4}\)

We know that:

\(\displaystyle 360^{\circ}=2\pi\) Radians

since the giving angle was in radians then we multiply

\(\displaystyle \frac{5\pi}{6}*\frac{180}{\pi}= 150^{\circ}\)

We know that:

\(\displaystyle 360^{\circ}=2\pi\) Radians

since the giving angle was in radians then we multiply

\(\displaystyle 3*\frac{180}{\pi}= 171.887^{\circ}\)