An oddshaped house in Asia is built at a
Guidance
The unit circle is the circle centered at the origin with radius equal to one unit. This means that the distance from the origin to any point on the circle is equal to one unit.
Using the unit circle, we can define another unit of measure for angles, radians. Radian measure is based upon the circumference of the unit circle. The circumference of the unit circle is
One radian is equal to the measure of
We can use the equality,
To convert from degrees to radians, multiply by
To convert from radians to degrees, multiply by
Example A
a. Convert
b. Convert
Solution:
a. To convert from degrees to radians, multiply by
b. To convert from radians to degrees, multiply by
Example B
Find two angles, one positive and one negative, coterminal to
Solution:
Since we are working in radians now we will add/subtract multiple of
Now, to find the reference angle, first determine in which quadrant
Consider
Example C
Find two angles coterminal to
Solution:
This time we will add multiples of
In this case
Concept Problem Revisit
To convert from degrees to radians, multiply by
Guided Practice
1. Convert the following angle measures from degrees to radians.
a.
b.
c.
2. Convert the following angle measures from radians to degrees.
a.
b.
c.
3. Find two coterminal angles to
Answers
1. a.
b.
c.
2. a.
b.
c.
3. There are many possible coterminal angles, here are some possibilities:
positive coterminal angle:
negative coterminal angle:
Using the coterminal angle,
Explore More
For problems 15, convert the angle from degrees to radians. Leave answers in terms of

135∘ 
240∘ 
−330∘ 
450∘ 
−315∘
For problems 610, convert the angle measure from radians to degrees.

7π3 
−13π6 
9π2 
−3π4 
5π6
For problems 1115, find two coterminal angles (one positive, one negative) and the reference angle for each angle in radians.

8π3 
11π4 
−π6 
4π3 
−17π6