9.9 Graphing Trig Functions with Amplitudes and Vertical ...
6.3 Graphing Trig Functions
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Transcript of 6.3 Graphing Trig Functions
6.3 Graphing Trig FunctionsLast section we analyzed graphs, now we will graph them.
Graph: y = sin θ - 1First, look at y = sin θ
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Since the – 1 is on the outside that means we are shifting DOWN ONE unit
Graph: y = cos θ + 2First, look at y = cos θ
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Since the + 2 is on the outside that means we are shifting UP TWO units
Graph: y = 4sin 2θ First, look at y = sin θ
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Amplitue = 4
Period = 360/2 = 180
Phase Shift = 0°I will change the period first
Then change the amplitude
Graph: y = -2cos (θ + 90°) First, look at y = cos θ
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Amplitue = 2
Period = 360/1 = 360
Phase Shift = Left 90°I will change the amplitude
first
Then change the phase shift
Graph: y = 2tan( θ +45)First, look at y = 2tan x
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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
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Graph: y = 2tan( θ +45)Continued Now let’s shift
45° tothe right
Graph: y = sin ( + 90°) See if you can graph this without graphing each step.
Amplitude = 1
Period = 360/½ = 720
Phase Shift = 180° Left
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θ2
(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
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
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y = tan 12 x( )Graph:
Graph: y = 3cos (θ - 90°) First, look at y = cos θ
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Amplitue = 3
Period = 360/1 = 360°
Phase Shift = 90°I will change the period first
Then change the amplitude
FIX THIS!!!
Graph: y = cot (θ – 90°) Cot 0 = Does Not Exist
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Amplitue = none
Period = 180/1 = 180°
Phase Shift = 90° Right
I will change the period first
Then change the amplitude
FIX THIS!!!
Graph: y = sin x + cos x
Best approach - table
θ cos θ
sin θ
sum
0° 1 0 145° .71 .71 1.490° 0 1 1135° -.71 .71 0180° -1 0 -1225° -.71 -.71 -1.4270° 0 -1 -1315° .71 -.71 0360° 1 0 1
Period = 360
Graph: y = cos 2x – cos x
Best approach - table
θ cos 2θ
cos θ -
0° 1 1 045° 0 .71 -.7190° -1 1 -1135° 0 -.71 .71180° 1 -1 2225° 0 -.71 .71270° -1 0 -1315° 0 .71 -.71360° 1 1 0
Period = ???
Graph: y = tan ( - )
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x2
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π8 Amplitude = 1
Period = 180/½ = 360
Phase Shift = π/4 right
Graph: y = 2sin x + 3cos x
Best approach - table
θ 3cos θ
2sin θ sum
0° 0 3 345° 1.4 2.1 3.590° 2 0 2135°
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???