1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.
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Transcript of 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.
![Page 1: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/1.jpg)
1.6 Graphing Trig FunctionsYesterday we focused on the Unit Circle, today we start graphing Trigs
![Page 2: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/2.jpg)
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
![Page 3: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/3.jpg)
Graph: y = sin θ - 1First, look at y = sin θ
1
-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/kPeriod of tan: π/k
![Page 4: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/4.jpg)
Graph: y = cos θ + 2First, look at y = cos θ
1
-1
Since the + 2 is on the outside that means we are shifting UP TWO units
![Page 5: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/5.jpg)
Graph: y = 4sin 2θFirst, look at y = sin θ
1
-1
Amplitue = 4
Period = 360/2 = 180
Phase Shift = 0°
I will change the period first
Then change the amplitude
![Page 6: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/6.jpg)
Graph: y = -2cos (θ + 90°)First, look at y = cos θ
1
-1
Amplitue = 2
Period = 360/1 = 360
Phase Shift = Left 90°I will change the amplitude
first
Then change the phase shift
![Page 7: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/7.jpg)
Graph: y = 2tan( θ +45)First, look at y = tan x
1
-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
![Page 8: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/8.jpg)
1
-1
Graph: y = 2tan( θ +45)
Continued Now let’s shift 45° tothe left
![Page 9: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/9.jpg)
NOW YOU TRY!!!
JUST PLOT POINTS!!!
![Page 10: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/10.jpg)
Graph: y = sin ( + 90°) See if you can graph this without graphing each step.
Amplitude = 1
Period = 360/½ = 720
Phase Shift = 180° Left
2
(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
![Page 11: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/11.jpg)
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
y tan 12 x Graph:
![Page 12: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/12.jpg)
Graph: y = 3cos (θ - 90°)
1
-1
Amplitude = 3
Period = 360/1 = 360°
Phase Shift = 90°
![Page 13: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/13.jpg)
Graph: y = cot (θ – 90°)Cot 0 = Does Not Exist
1
-1
Amplitue = none
Period = 180/1 = 180°
Phase Shift = 90° Right
![Page 14: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/14.jpg)
Graph: y = cos x + sin x
Best approach - table
θ cos θ
sin θ
sum
0° 1 0 1
45° .71 .71 1.4
90° 0 1 1
135° -.71 .71 0
180° -1 0 -1
225° -.71 -.71 -1.4
270° 0 -1 -1
315° .71 -.71 0
360° 1 0 1
Period = 360
![Page 15: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/15.jpg)
Graph: y = cos 2x – cos x
Best approach - table
θ cos 2θ
cos θ -
0° 1 1 0
45° 0 .71 -.71
90° -1 1 -1
135° 0 -.71 .71
180° 1 -1 2
225° 0 -.71 .71
270° -1 0 -1
315° 0 .71 -.71
360° 1 1 0
Period = ???
![Page 16: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/16.jpg)
Graph: y = tan ( - )
x
2
8 Amplitude = 1
Period = 180/½ = 360
Phase Shift = π/4 right
![Page 17: 1.6 Graphing Trig Functions Yesterday we focused on the Unit Circle, today we start graphing Trigs.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649edb5503460f94bea587/html5/thumbnails/17.jpg)
Graph: y = 3cos x + 2sin x
Best approach - table
θ 3cos θ
2sin θ sum
0° 0 3 3
45° 1.4 2.1 3.5
90° 2 0 2
135°
1.4 -2.1 -.7
180°
0 -3 -3
225°
-1.4 -2.1 -3.5
270°
-2 0 -2
315°
-1.4 2.1 .7
360°
0 3 3
Period = 360???