RADIANS

Radians are important in the unit circle, because they are used to express angle measures.
First, a radian is the ratio between the radius of a circle and the arc of the same length (imagine bending the radius and fitting it on the circumference of the circle.

the angle formed is 1 radian.

Rember that the circumference of a circle is 2Pi(radius). Since the radius is equal to the arc length, you can say that 360 degrees=2Pi(radian).

Now. divide each side by 2Pi. You get:

1 Radian=180/Pi degrees.

You can also divide by 360:

1 degree=Pi/180 (radian)

Now to convert radians into angles...

you already know that 360 degrees=2 Pi (radian)

which means that 180 degrees=Pi (radian) *divide 360 and 2Pi by 2*

which means that 90 degrees=Pi/2 (radian) *divide 180 and Pi by two*

If you want to know the radian of a 30 degree angle:

substitute 30 into 1 degree=Pi/180 (radian)

30 degrees=30Pi/180 (radian)

which reduces to: 30 degrees=Pi/6 (radian)

 Using 1 degree=Pi/180 (radian), you can find the radian measure of any angle measure you want!

If you want to know the degree of a Pi/6 radians:

substitute Pi/6 (radian) into 1 Radian=180/Pi degrees

Pi/6 radian=180Pi/6Pi degrees

which reduces to: Pi/6 radian=30 degrees

Using 1 Radian=180/Pi (degrees), you can find the degree measure of any radian you want!