Trigonometric Functions: The Unit Circle

1. Trigonometric Functions: The Unit Circle Section 4.2

2. Objectives • Find a point on the unit circle given one coordinate and the quadrant in which the point lies. • Determine the coordinates of a point on the unit circle given a point on the unit circle. • State the sign of the sine or cosine value of an angle based on the quadrant in which the terminal side of an angle occurs. • State the sine and cosine values of an angle (measured in radians) where the angles have a measure of

3. Objectives • Determine the tangent, cotangent, secant, and cosecant values of an angle given a point on the unit circle. • State the sign of the tangent, cotangent, secant, and cosecant value of an angle based on the quadrant in which the terminal side of an angle occurs. • Determine the tangent, cotangent, secant, and cosecant values of an angle (measured in radians) where the angles have a measure of

4. Vocabulary • quadrant • sine of an angle • cosine of an angle • terminal side of an angle • initial side of an angle • tangent of an angle • cotangent of an angle • secant of an angle • cosecant of an angle

5. Unit Circle

6. If the point is on the unit circle in quadrant IV, then find y.

7. If P(t) has coordinates (0.141, 0.99), find the coordinates of each point indicated below.

8. Find the terminal point P(x, y) on the unit circle determined by the value of

9. If , find the sin(t) and cos(t).

10. If , find the sin(t) and cos(t).

11. If , find the sin(t) and cos(t).

12. Quotient Identities

13. Reciprocal Identites

14. Pythagorean Identity