1. Sullivan Precalculus: Section 5.2 Trig Functions: Unit Circle
Objectives of this Section
Find the Exact Value of the Trigonometric Functions Using the Unit Circle
Find the Exact Value of the Trigonometric Functions of 45 Degrees
Find the Exact Value of the Trigonometric Functions of 30 Degrees and 60 Degrees
Use a Calculator to Approximate the Value of the Trigonometric Functions of Acute Angles

2. The unit circle is a circle whose radius is 1 and whose center is at the origin.
Since r = 1:
becomes

3. y
(0, 1) x
(-1, 0)
(1, 0)
(0, -1)

4. y
(0, 1)
P = (a, b) x
(-1, 0)
(1, 0)
(0, -1)

5. Let t be a real number and let P = (a, b) be the point on the unit circle that corresponds to t.
The sine function associates with t the y-coordinate of P and is denoted by
The cosine function associates with t the x-coordinate of P and is denoted by

9. y
(0, 1)
P = (a, b) x
(-1, 0)
(1, 0)
(0, -1)

11. Find the exact value of the six trigonometric functions of 45 degrees.
b = 1
a = 1

13. Find the exact value of the six trigonometric functions of 30 and 60 degrees.2 2 b a a
2a = 2 so a = 1