Section 5.2 Trigonometric Functions of Real Numbers Objectives: Compute trig functions given the terminal point of a real number. State and apply the reciprocal.

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Presentation transcript:

Section 5.2 Trigonometric Functions of Real Numbers Objectives: Compute trig functions given the terminal point of a real number. State and apply the reciprocal and Pythagorean identities of trig functions.

Class Work Fill out the unit circle.

Definition of the Trigonometric Functions Let t be any real number and let P(x,y) be the terminal point on the unit circle determined by t. We define

Ex 1. Find the six trig functions of each given real number t. a) b)

Signs of Trig Functions QuadrantPositive I II III IV

Ex 2 Determine the sign of the following trig functions. a) b) c)

Class Work Find the six trig functions of each given real number t. 1.2.

Determine the sign of the following trig functions

Ex 3 Find the exact value of the trig function at the given real number t. a) b) c)

Ex 4. Use your calculator to find an approximate value of the trig function at t. (Your calculator must be in radian mode!!) a) b) c) d)

Class Work Find the exact value of the trig function at the given real number t

Use your calculator to find an approximate value

Fundamental Identites

Ex 5. If and t is in quadrant IV, find the values of all the trig functions at t.

Ex 6. Write tan t in terms of cos t, where t is in quadrant III.

Ex 7. Write cos t in terms of sin t, where t is in quadrant IV.

Ex 8 Write csc t in terms of cot t, where t is in quadrant III.

Class Work Find the values of all the trig functions of t from the given information. 13. In quad III 14. In quad III 15. sint < 0

Write the first expression in terms of the second if the terminal point is in the given quadrant. 16. tan t, cos t quad III 17. sin t, sec t quad IV

HW #2 p eoo, all, 27-35eoo, odd