Pre-Calc Book Section 5.2 Trigonometric Functions of Real Numbers Objectives: How do you find the value of any given trig angle? How can understanding the signs of the quadrants help in finding the function value of any trig angle?

Trigonometric Functions of Any Angle  

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

Ex. 2 Let be a point on the terminal side of  Ex.2 Let be a point on the terminal side of . Find the sine, cosine, and tangent of .

Ex. 3 Let (-3,4) be a point on the terminal side of  Ex.3 Let (-3,4) be a point on the terminal side of . Find the sine, cosine, and tangent of .

Signs of Trig Functions Quad Positive I II III IV All Trig. Functions Sine/Cosecant Tangent/Cotangent Cosine/Secant All Students Take Calculus

Ex. 4 Determine the sign of the following trig functions. a) b) c) > 0, because the terminal point of is in Quad I > 0, because the terminal point of is in Quad III < 0, because the terminal point of is in Quad IV

Class Work Find the six trig functions of each given real number t. 1. 2.

Determine the sign of the following trig functions. 3. 4. 5.

Ex 5. Evaluate the sine, cosine and tangent of the given angle.

Ex. 6 Find the exact value of the trig function at the given real number t.

Class Work Find the exact value of the trig function at the given real number t. 6. 7. 8.

Ex.7 State the quadrant in which  lies.

Fundamental Identites

Ex 8. If and t is in quadrant IV, find the values of all the trig functions at t.

Ex 9. Find the values of the six trig functions of  in the given quadrant.

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

HW #3 p.416 3-19 eoo, 27-35 eoo, 63-69 odd