1.6 Graphing Trig FunctionsYesterday we focused on the Unit Circle, today we start graphing Trigs

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

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

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

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

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

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

1

-1

Graph: y = 2tan( θ +45)

Continued Now let’s shift 45° tothe left

NOW YOU TRY!!!

JUST PLOT POINTS!!!

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

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:

Graph: y = 3cos (θ - 90°)

1

-1

Amplitude = 3

Period = 360/1 = 360°

Phase Shift = 90°

Graph: y = cot (θ – 90°)Cot 0 = Does Not Exist

1

-1

Amplitue = none

Period = 180/1 = 180°

Phase Shift = 90° Right

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

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 = ???

Graph: y = tan ( - )

x

2

8 Amplitude = 1

Period = 180/½ = 360

Phase Shift = π/4 right

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???