1. Precalculus 4.5 Graphs of Sine and Cosine 1 Bellwork 60° 13 Find the two sides of this triangle.

2. Precalculus 4.5 Graphs of Sine and Cosine Objectives: Sketch the graphs of basic sine and cosine functions Use amplitude and period to sketch the graphs Sketch translations of graphs

3. Precalculus 4.5 Graphs of Sine and Cosine 3 Basic Sine and Cosine Curves

4. Precalculus 4.5 Graphs of Sine and Cosine 4 Example ·Sketch the graph of y=2sinx on the interval [-π, 4π]

5. Precalculus 4.5 Graphs of Sine and Cosine 5 Amplitude and Period ·The amplitude is half the distance between the maximum and minimum values of the function ·The period is the distance in x needed for the function to complete one cycle

6. Precalculus 4.5 Graphs of Sine and Cosine 6 Standard Form of Sine and Cosine Functions · · ·The amplitude = |a| ·The period = 2π/b ·Horizontal shifts are caused by c ·Interval left endpoint: solve bx-c=0 ·Interval right endpoint: solve bx-c=2π ·Vertical shifts are caused by d

7. Precalculus 4.5 Graphs of Sine and Cosine 7 Steps to Graph ·Find amplitude ·Find left endpoint ·bx-c=0 ·Find right endpoint ·bx-c=2π ·Find the period · 2π/b ·Find key points by: ·Dividing period-interval into four equal parts ·Add “period/4” starting with left endpoint of the interval

8. Precalculus 4.5 Graphs of Sine and Cosine 8 Example ·Graph ·Endpoints: ·Period: ·Amplitude: ·Key points:

9. Precalculus 4.5 Graphs of Sine and Cosine 9 Example ·Graph ·Endpoints: ·Period: ·Amplitude: ·Key points:

10. Precalculus 4.5 Graphs of Sine and Cosine 10 Example ·Graph ·Endpoints: ·Period: ·Amplitude: ·Key points:

11. Precalculus 4.5 Graphs of Sine and Cosine 11 Closure ·Describe the basic shape of the sine graph and the cosine graph ·Sine starts at zero going up ·0,1,0,-1,0 ·Cosine starts at one going down ·1,0,-1,0,1

12. Precalculus 4.5 Graphs of Sine and Cosine 12 Homework ·Label Assignment: HW 4.5 ·Pg. 330: #1-14 all, #16-26 even, #27-33 odds