1. 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?

2. Trigonometric Functions of Any Angle

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

4. 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 .

5. 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 .

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

7. 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

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

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

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

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

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

14. Ex.7 State the quadrant in which  lies.

15. Fundamental Identites

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

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

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

19. HW #3 p eoo, eoo, odd