1. Chapter 4 Trigonometry Day 2 (Covers a variety of topics in 4.2-4.4) 6 Notecards

2. Six Trig Functions These are the reciprocal functions Six Trig Functions (continued on next slide)

3. To remember your trig functions: SOHCAHTOA Another Trig Property you need to know:

4. Ex 1: sin  = 3/5 Find the other trig functions: cos  = _______ tan  = _______ csc  = ________ sec  = ________ cot  = ________ 

5.  Ex 2: Find the other trig functions: sin  = _______ cos  = _______ csc  = ________ sec  = ________ cot  = ________

6. Suppose I give you a point on the Unit Circle: Any point on a unit circle (when radius is 1) is in the form (cos,sin) Therefore: tan  = ______ csc  = ______ sec  = ______ cot  = _____ 

7. Basic Trig Functions 1 2 60° 30° 1 1

8. DegreesRadiansSinCostan 30 45 60

9. (1,0) (0,1) (-1,0) (0,-1) 90° 180° 270° 0°/360° Use the unit circle, with a radius of 1, to figure out your trig functions for the Quadrant angles 0,90,180,270,360 Remember: And that all points on a unit circle are in the form of

10. AS TC When doing Trig Functions in each quadrant, some functions ( and their reciprocals) are positive and some might be negative: Here is the phrase to remember this in the quadrants: A ll S tudents T ake C alculus Signs (+/-) of Trig functions in Quadrants Continued on next slide

11. “A” means that in the first quadrant all the trig functions are positive: SIN, COS, TAN “S”means that in the second quadrant only the SIN is positive, and the COS and TAN are negative “T” means that in the third quadrant only the TAN is positive, and the SIN and COS are negative “C” means that in the fourth quadrant only the COS is positive, and the TAN and SIN are negative Continued from previous slide

12. Reference Angles You will use reference angles to help you figure out the value of trig functions Your reference angle is the angle between the terminal side and either the 180° line or the 0°/360° line Reference Angles

13. Find the reference angle for the following:

14. Even and Odd Trig Functions Cosine and Secant are EVEN: cos(-t) = cos (t)sec(-t) = sec (t) Sine, Cosine, Tangent, and Cotangent are ODD: sin(-t) = - sin(t) csc(-t) = - csc(t) tan(-t) = - tan(t)cot(-t) = - cot(t) For example: sin(t) = 1/5, so sin(-t) = -1/5 If cos(t) = 2/3, then cos(π+t) = -2/3