1. Precalculus Functions & Graphs Unit Circle – A unit circle is a circle whose radius is one unit. 5.3A Trigonometric Functions of Real Numbers

2. Precalculus Functions & Graphs Point P(x, y) is shown on the unit circle U corresponding to a real number t. Find the values of the trigonometric functions at t. 5.3A Trigonometric Functions of Real Numbers Example #1

3. Precalculus Functions & Graphs Point P(x, y) is shown on the unit circle U corresponding to a real number t. Find the values of the trigonometric functions at t. 5.3A Trigonometric Functions of Real Numbers You Try #1

4. Precalculus Functions & Graphs Remember the rotation and reflection rules from earlier in the year and Geometry. 5.3A Trigonometric Functions of Real Numbers Example #2

5. Precalculus Functions & Graphs 5.3A Trigonometric Functions of Real Numbers Example #2 Negative t means reflect over x axis Reflect over x axis then move 180 clockwise

6. Precalculus Functions & Graphs 5.3A Trigonometric Functions of Real Numbers You Try #2 Negative t means reflect over x axis Reflect over x axis then move 180 clockwise

7. Precalculus Functions & Graphs Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P and the exact values of the trigonometric functions of t whenever possible. 5.3A Trigonometric Functions of Real Numbers Example #3

8. Precalculus Functions & Graphs Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P and the exact values of the trigonometric functions of t whenever possible. 5.3A Trigonometric Functions of Real Numbers You Try #3

9. Precalculus Functions & Graphs Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P and the exact values of the trigonometric functions of t whenever possible. 5.3A Trigonometric Functions of Real Numbers Example #4 QIV so cos & sec positive

10. Precalculus Functions & Graphs Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P and the exact values of the trigonometric functions of t whenever possible. 5.3A Trigonometric Functions of Real Numbers You Try #4 QII so sin & csc positive