1. 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs

2. How will we graph??? On a homework, quiz, or test you will just simply PLOT POINTS But in this powerpoint, we are going to discuss what the graph should look like so you know before you graph and how to check yourself afterwards

3. Graph: y = sin θ - 1 First, look at y = sin θ 1 Since the – 1 is on the outside that means we are shifting DOWN ONE unit Domain: (-∞, ∞) Range: [-2, 0] Period: 2π Amplitude: 1 General form of trig equations: y = ±Asin(kθ – C) Period for sin or cos: 2π/k Period of tan: π/k

4. Graph: y = cos θ + 2 First, look at y = cos θ 1 Since the + 2 is on the outside that means we are shifting UP TWO units

5. Graph: y = 4sin 2θ First, look at y = sin θ 1 Amplitue = 4 Period = 360/2 = 180 Phase Shift = 0° I will change the period first Then change the amplitude

6. Graph: y = -2cos (θ + 90°) First, look at y = cos θ 1 Amplitue = 2 Period = 360/1 = 360 Phase Shift = Left 90° I will change the amplitude first Then change the phase shift

7. Graph: y = 2tan( θ +45) First, look at y = tan x 1 Since 2 in front changes the “amplitude”?? Then each output is doubled Asymptotes are still 90° + 180k° We’re not done, go to next slide

8. 1 Graph: y = 2tan( θ +45) Continued Now let’s shift 45° to the left

9. NOW YOU TRY!!! JUST PLOT POINTS!!!

10. Graph: y = sin ( + 90°) See if you can graph this without graphing each step. Amplitude = 1 Period = 360/½ = 720 Phase Shift = 180° Left (π,0) (2π,-1)(3π,0) (4π,1) (5π,0) (0,1) Θ 0 90 180 270 360 450 540 630 720 y 1 0.7 0 -0.7 -1 -0.7 0 0.7 1

11. See if you can graph this without graphing each step. Amplitude = 1 Period = 180/½ = 360 Phase Shift = 0° Θ 0 90 180 270 360 450 540 630 720 y 0 1 UD -1 0 1 UD -1 0 Graph:

12. Graph: y = 3cos (θ - 90°) 1 Amplitude = 3 Period = 360/1 = 360° Phase Shift = 90°

13. Graph: y = cot (θ – 90°) Cot 0 = Does Not Exist 1 Amplitue = none Period = 180/1 = 180° Phase Shift = 90° Right

14. Graph: y = cos x + sin x Best approach - table θ cos θ sin θsum 0°101 45°.71 1.4 90°011 135°-.71.710 180°0 225°-.71 -1.4 270°0 315°.71-.710 360°101 Period = 360

15. Graph: y = cos 2x – cos x Best approach - table θcos 2θ cos θ- 0°110 45°0.71-.71 90°1 135°0-.71.71 180°12 225°0-.71.71 270°0 315°0.71-.71 360°110 Period = ???

16. Graph: y = tan ( - ) Amplitude = 1 Period = 180/½ = 360 Phase Shift = π/4 right

17. Graph: y = 3cos x + 2sin x Best approach - table θ3cos θ 2sin θsum 0°033 45°1.42.13.5 90°202 135°1.4-2.1-.7 180°0-3 225°-1.4-2.1-3.5 270°-20 315°-1.42.1.7 360°033 Period = 360???