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I. Model Problems.
II. Practice
III. Challenge Problems
IV. Answer Key
V. Unit Circle Fill In the Blank
VI. Unit Circle Filled In
Web Resources

 Unit Circle Game
 Graph and Formula of the Unit Circle
Unit Circle Printables (fill in the blank unit circle)
 Graph of Sine to Unit Circle
 Finding the Reference Angle
 Converting Radians to Degrees
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Unit Circle
I. Model Problems
Unit Circle: circle on coordinate plane with center
with radius equal to 1.
terminal side
The angel, , is positive measured counterclockwise from x- axis counter-clockwise to terminal
side. The angel, , is negative measured clockwise from x- axis counter-clockwise to terminal
side.
Radian measure of an angle is the arc length of angle on a unit circle.
Reference angel is the measure of the angle from terminal side to x-axis. The reference angel is
always less than or equal to 90°
.
reference angles
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In these examples we will change from degree to radian measures.
Example 1: Change 210° to radian measure.
; Because we want to cancel the
degree measure use the conversion factor
Simplify.
Answer:
Example 2: Change to degree measure.
; Because we want to cancel the
radian measure use the conversion factor
Simplify.
Answer:
In this example we will find the angle given the terminal side’s endpoint on the unit circle.
Example 3: Find the angle determined by a terminal side with endpoint
.
Draw triangle of terminal side. Radius equals
1. Height equals .
Find reference angle using trig functions.
The angle is
Use reference angle to find angle to terminal
side.
Answer:
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II. Practice Problems
Change from degree to radian measure.
1.
2.
3.
4.
5.
6.
Change from radian to degree measure.
7.
8.
9.
10.
11.
12.
Find the measure of the angle determined by the endpoint of the terminal side on the unit
circle.
13.
14.
15.
16.
17.
18.
Given
terminal side.
find the following for the given endpoint of the
19.
20.
21.
22.
III. Challenge Problems
23. For each quadrant on the coordinate plane determine whether sine, cosine, and tangent
are positive or negative.
24. For each axes determine the value of sine, cosine, and tangent.
25. Prove
.
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IV. Answers
21. Undefined
1.
22.
2.
Challenge Problems
3.
23. Quadrant I: sine, cosine, tangent are
positive. Quadrant II: sine is positive;
cosine, tangent are negative. Quadrant
III: tangent is positive; sine, cosine are
negative. Quadrant IV: cosine is
positive; sine, tangent are negative.
4.
5.
6.
7. 150°
24. positive x: sine=0, cosine=1, tangent=0;
positive y: sine=1, cosine=0, tangent is
undefined; negative x: sine=0, cosine=
−1, tangent=0; negative y: sine= −1,
cosine=0, tangent= −1;
8. 225°
25.
9. 360°
10. 120°
11. 270°
12. 315°
13. 135°
14. 210°
15. 300°
16. 270°
17. 225°
18. 330°
19.
20.
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