1. SECTION 2.3 EQ: Which of the trigonometric functions are positive and which are negative in each of the four quadrants?

2. Warm-Up/Activator Name the quadrants of the Coordinate (Cartesian) Plane – use drawing on next slide. Label the signs of x and y in each quadrant Which coordinate is sin and which coordinate is cos ? Label the signs of the sine and cosine in each quadrant.

3. Drawing for the Warm-up/Activator

4. So, by multiplying the top and bottom of the fraction by 1/H it follows that How does tangent relate to sine and cosine?

5. + + -- - + A C T S P(cosΘ, sinΘ) ( x, y ) ALL STUDENTS TAKE CALCULUS

6. Reference Right Triangle Drop a perpendicular from the terminal side to the x-axis and then you have a right triangle with the reference angle as one of the acute angles.

7. Starter Examples: Find the reference angle for each of the following, then determine the value of the function based on special or quadranal angles, and the location of the terminal side. 1) sin 300 ref < 60 Sign - - sin 60 2)cos 150 30 - - cos 30 3) tan 225 45 + tan 45 1

8. Example 4 Find the reference angle for each angle given. (a) 210˚ (b) 135˚ (c) 422˚

9. Your Turn 4 Find the reference angle for each angle given. (a) 160˚ (b) 285˚ (c) 600˚

10. Example 5 & Your Turn 5 Find the exact value of cos 210˚ Find the exact value of sin 330˚

11. Example 6 & Your Turn 6 Find the exact value of tan 495˚ Find the exact value of tan 660˚

12. Example 7 & Your Turn 7 Find the exact value of csc (-210˚) Find the exact value of sec (-330˚)

13. Example 8 & Your Turn 8 Find all values of where when Find all values of where when

14. Example 9 & Your Turn 9 Use a calculator to approximate the following a) tan 466˚b) csc (-313˚) Use a calculator to approximate the following a) sec (-118˚)b) cot (226˚)

15. Example 10 & Your Turn 10