1. 6.3 Graphing Trig Functions
Last section we analyzed graphs, now we will graph them.

2. Graph: y = sin θ - 1 First, look at y = sin θ
Since the – 1 is on the outside that means we are shifting DOWN ONE unit 1 -1

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

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

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

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

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

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

9. Graph:
See if you can graph this without graphing each step.
Amplitude = 1
Period = 180/½ = 360
Phase Shift = 0° Θ
y UD UD

10. Graph: y = 3cos (θ - 90°) First, look at y = cos θ Amplitue = 3
FIX THIS!!!
Amplitue = 3
Period = 360/1 = 360°
Phase Shift = 90°
I will change the period first 1
Then change the amplitude -1

11. Graph: y = cot (θ – 90°) Cot 0 = Does Not Exist FIX THIS!!!
Amplitue = none
Period = 180/1 = 180°
Phase Shift = 90° Right
I will change the period first 1
Then change the amplitude -1

12. Graph: y = sin x + cos x Best approach - table θ cos θ sin θ sum 0° 1
45°
.71
1.4
90°
135°
-.71
180° -1
225°
-1.4
270°
315°
360°
Period = 360

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

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

15. Graph: y = 2sin x + 3cos x Best approach - table θ 3cos θ 2sin θ sum0° 3
45°
1.4
2.1
3.5
90° 2
135°
-2.1
-.7
180° -3
225°
-1.4
-3.5
270° -2
315° .7
360°
Period = 360???