In which quadrant does the terminal side of the angle
Guidance
Angles of rotation are formed in the coordinate plane between the positive
Since the
An angle of rotation can be described infinitely many ways. It can be described by a positive or negative angle of rotation or by making multiple full circle rotations through
For the angle
Example A
Determine two coterminal angles to
Solution:
To find coterminal angles we simply add or subtract
More Guidance
A
reference angle
is the acute angle between the terminal side of an angle and the
Note: A reference angle is never determined by the angle between the terminal side and the
Example B
Determine the quadrant in which
Solution:
Since our angle is more than one rotation, we need to add
Now we can plot the angle and determine the reference angle:
Note that the reference angle is positive
Example C
Give two coterminal angles to
Solution:
To find the coterminal angles we can add/subtract
By plotting any of these angles we can see that the terminal side lies in the third quadrant as shown.
Since the terminal side lies in the third quadrant, we need to find the angle between
Concept Problem Revisit
Since our angle is more than one rotation, we need to add
If we plot this angle we see that it is
Now determine the reference angle:
Guided Practice
1. Find two coterminal angles to
2. Find the reference angle for
3. Find the reference angle for
Answers
1.
2.
3.
Explore More
Find two coterminal angles to each angle measure, one positive and one negative.

−98∘ 
475∘ 
−210∘ 
47∘ 
−1022∘ 
354∘ 
−7∘
Determine the quadrant in which the terminal side lies and find the reference angle for each of the following angles.

102∘ 
−400∘ 
1307∘ 
−820∘ 
304∘ 
251∘ 
−348∘ 
Explain why the reference angle for an angle between
0∘ and90∘ is equal to itself.