RADIAN and DEGREE MEASURE
By Daniel William Smith and Colin Adam Robertson
We would like to apologize for the lack of visuals. We had some technical difficulties with our video, and not everyone can be talented enough to make a song about radians and degrees.

Basically, there are two ways to measure angles: radians and degrees.

RADIANS
I can't get this off of bold, so whatever. Anyway, a radian is the measure of a central angle in a circle that extends out to an arc of a circle, and it must be the same length as the radius. Because the circumference of a circle is 2 times pi times the radius, the measure of a full circle is 2 times pie radians (im not sure how to do the pi symbol, sorry).

So, one half of one revolution is 2pi/2, simplified to pi
A quarter of one revolution is 2pi/4, which is pi/2 and so on.

To find the coterminal angles of any angle, you must either subtract 2 pi (positive coterminal) or add 2 pi (negative coterminal). A good rule of thumb is to do the opposite system of what they are asking for (subtract for positive and add for negative). For example the angle -2pi/3 has a negative coterminal angle of 4pi/3 (-2pi/3 + 2pi= 4pi/3)
(above: complement/ supplement angles) To find the compliment or supplement of an angle, subtract your angle from pi/2 or pi respectively. For example, to find the supplement of the angle pi/2, subtract pi/2 from pi to get pi/2 (pi- pi/2=pi/2)

Note: Angles between 0 & pi/2 are acute and angles between pi/2 & pi are obtuse.

DEGREES
A degree is another way to measure central angles of circles. Instead of there being 2pi radians in a revolution there are 360 degrees. Therefore....

A half revolution is 180 degrees
A quarter revolution is 90 degrees and so on.

CONVERTING RADIANS TO DEGREES/DEGREES TO RADIANS

To convert radians to degrees multiply the radians by (180 degrees)/pi
This cancels out the pi's (radians are already unitless) and gives the answer units of degrees

For Example:
Multiply 3pi/4 by 180 degrees/pi and you will get 135 degrees

And to convert degrees to radians multiply the degrees by pi/(180 degrees)
This cancels out the degrees and puts the answer in terms of pi and in radians.

For Example:
Multiply 270 degrees by pi/180 degrees and you will get 3pi/2 radians.

Example Problems:
1. Find the positive coterminal angle of the angle 11pi/6.
2. Find the negative coterminal angle of the angle 5pi/6.

3. Find the complement of the angle 2pi/5.
4. Find the supplement of the angle 3pi/4.

5. Convert 120 degrees into radians.
6. Convert 2pi/5 radians into degrees.

RADIAN and DEGREE MEASUREBy Daniel William Smith and Colin Adam Robertson

We would like to apologize for the lack of visuals. We had some technical difficulties with our video, and not everyone can be talented enough to make a song about radians and degrees.

Basically, there are two ways to measure angles: radians and degrees.

RADIANS

I can't get this off of bold, so whatever. Anyway, a radian is the measure of a central angle in a circle that extends out to an arc of a circle, and it must be the same length as the radius. Because the circumference of a circle is 2 times pi times the radius, the measure of a full circle is 2 times pie radians (im not sure how to do the pi symbol, sorry).

So, one half of one revolution is 2pi/2, simplified to pi

A quarter of one revolution is 2pi/4, which is pi/2 and so on.

To find the coterminal angles of any angle, you must either subtract 2 pi (positive coterminal) or add 2 pi (negative coterminal). A good rule of thumb is to do the opposite system of what they are asking for (subtract for positive and add for negative). For example the angle -2pi/3 has a negative coterminal angle of 4pi/3 (-2pi/3 + 2pi= 4pi/3)

(above: complement/ supplement angles)

To find the compliment or supplement of an angle, subtract your angle from pi/2 or pi respectively. For example, to find the supplement of the angle pi/2, subtract pi/2 from pi to get pi/2 (pi- pi/2=pi/2)

Note: Angles between 0 & pi/2 are acute and angles between pi/2 & pi are obtuse.

DEGREES

A degree is another way to measure central angles of circles. Instead of there being 2pi radians in a revolution there are 360 degrees. Therefore....

A half revolution is 180 degrees

A quarter revolution is 90 degrees and so on.

CONVERTING RADIANS TO DEGREES/DEGREES TO RADIANS

To convert radians to degrees multiply the radians by (180 degrees)/pi

This cancels out the pi's (radians are already unitless) and gives the answer units of degrees

For Example:

Multiply 3pi/4 by 180 degrees/pi and you will get 135 degrees

And to convert degrees to radians multiply the degrees by pi/(180 degrees)

This cancels out the degrees and puts the answer in terms of pi and in radians.

For Example:

Multiply 270 degrees by pi/180 degrees and you will get 3pi/2 radians.

Example Problems:

1. Find the positive coterminal angle of the angle 11pi/6.

2. Find the negative coterminal angle of the angle 5pi/6.

3. Find the complement of the angle 2pi/5.

4. Find the supplement of the angle 3pi/4.

5. Convert 120 degrees into radians.

6. Convert 2pi/5 radians into degrees.

Answers (steps included):

1. -pi/6 (11pi/6-2pi; 11pi/6-12pi/6; -pi/6)

2.17pi/6 (5pi/6+2pi; 5pi/6 +12pi/6; 17pi/6)

3. pi/10 (pi/2-2pi/5; 5pi/10-4pi/10;pi/10)

4. pi/4 (pi-3pi/4; 4pi/4-3pi/4; pi/4)

5. 2pi/3 (120/1 x pi/180)

6. 72 degrees (2pi/5 x 180/pi)