6.3 Graphing Trig Functions

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Presentation transcript:

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 Since the + 2 is on the outside that means we are shifting UP TWO units 1 -1

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

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

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

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

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 y 1 0.7 0 -0.7 -1 -0.7 0 0.7 1 (0,1) (4π,1) (5π,0) (π,0) (2π,-1) (3π,0)

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

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

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

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

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 = ???

Graph: y = tan ( - ) 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° 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???