1. Convert to radians/degrees. -80° 2) 450° 3) 𝟒𝝅 𝟑 4) 𝟑𝝅 𝟒
Warm Up
Convert to radians/degrees.
-80° 2) 450°
3) 𝟒𝝅 𝟑 4) 𝟑𝝅 𝟒
−𝟒𝝅 𝟗
𝟓𝝅 𝟐
𝟐𝟒𝟎°
𝟏𝟑𝟓°

2. Today’s Objective: I can graph the sine function.

3. 𝑓 𝑥 = sin 𝑥 x y
𝜋 6
𝜋 2
5𝜋 6 𝜋

4. 𝑦= sin 𝑥 𝑦= sin 𝜃 OR Domain: All real numbers Range: Period:
Amplitude:
All real numbers
– 1 ≤ y ≤ 1 2π 1

5. Period of a Sine Curve 𝑌 1 = sin 𝑥 𝑌 3 = sin .5𝑥 𝑌 2 = sin 4𝑥
Calculator
[MODE]: Radians
[WINDOW]
Xmin = 0
Xmax = 2π
Xscl = π/2
Ymin = – 2
Ymax = 2
Yscl = 0.5
b = # of cycles from 0 to 2π
Period of function = 2𝜋 𝑏
𝑦= sin 𝑏𝑥

6. Amplitude of a Sine Curve
Calculator
[MODE]: Radians
[WINDOW]
Xmin = 0
Xmax = 2π
Xscl = π/2
Ymin = – 2
Ymax = 2
Yscl = 0.5
𝑎 = amplitude (stretch)
– a = reflects graph across x-axis
𝑦=𝑎 sin 𝑥

7. Find amplitude and period for each equation.
1. 𝑦=2 sin 3𝑥
2. 𝑦= 1 2 sin 𝑥 4
1 2 or 0.5
Amplitude =
2𝜋 3
Amplitude = 2
Period =
2𝜋 0.25
Period =
=8𝜋
3..
Amplitude =
Period =
Write an equation for the graph. 3
4𝜋 3
= 2𝜋 𝑏
𝑦=3 sin 3 2 𝑥

8. Sketching a Sine Curve Graph
Amplitude = 2
Find amplitude and period.
Plot 5 points: Midline points Beginning, End Middle
Amplitude points Max Min
3. Sketch curve.
𝑦=2 sin 2𝑥
2𝜋 2 =𝜋
Period =
5 points: midline – max– midline – min – midline

9. p. 856: 27-35 odd Sketching a Sine Curve Graph Amplitude = 1.5
Find amplitude and period.
Plot 5 points
Sketch curve.
𝑦=1.5 sin 𝜋 2 𝑥
2𝜋 𝜋 2
Period = =4
5 points: midline – max– midline – min – midline
p. 856: odd

10. Today’s Objective: I can graph the cosine function.

11. 𝑦= cos 𝑥 𝑦= 𝑐𝑜𝑠 𝜃 OR Domain: All real numbers Range: Period:
Amplitude:
All real numbers
– 1 ≤ y ≤ 1 2π
How does this graph differ from y = sin x?
Translated left by 1
𝜋 2

12. W.S. 13.4/13.5 Sine and Cosine Function
Properties of Cosine Function
𝑎 = amplitude
– a = reflects graph across x-axis
b = # of cycles from 0 to 2π
Period of function = 2𝜋 𝑏
𝑦=𝒂 cos 𝒃𝑥
W.S. 13.4/13.5 Sine and Cosine Function
Sketch the graph of:
5 points: max – midline – min – midline - max
𝑦=𝟏.𝟓 cos 𝟐𝑥
𝑦=𝟐 cos 𝑥 𝟑