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6.3 Graphing Trig Functions

6.3 Graphing Trig Functions. Last section we analyzed graphs, now we will graph them. 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. Graph: y = cos θ + 2. First, look at y = cos θ.

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6.3 Graphing Trig Functions

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  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 = cosθ + 2 First, look at y = cosθ 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 = cosθ Amplitue = 2 Period = 360/1 = 360 Phase Shift = Left 90° I will change the amplitude first 1 -1 Then change the phase shift

  6. 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 ( + 90°) See if you can graph this without graphing each step. Amplitude = 1 Period = 360/½ = 720 Phase Shift = 180° Left Θ 0 90 180 270 360 450 540 630 720 y1 0.7 0 -0.7 -1 -0.7 0 0.7 1 (0,1) (4π,1) (5π,0) (2π,-1) (3π,0) (π,0)

  9. Graph: 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

  10. Graph: y = 3cos (θ - 90°) First, look at y = cosθ Amplitue = 3 Period = 360/1 = 360° Phase Shift = 90° FIX THIS!!! 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 + cosx Best approach - table Period = 360

  13. Graph: y = cos 2x – cosx Best approach - table 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 Period = 360???

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