Unit 4.5 Review By: Evan Mickelson LT: I can graph sine and cosine curves.

Learning Target: I can graph sine and cosine curves. Pages

Vocab Intercept: the point that the function touches an axis Minimum: smallest value of the function Maximum: largest value of the function Translation: when a function is moved but not changed in any other way Vertical stretch: pulling the graph away from the x-axis Horizontal stretch: pulling the graph away from the y-axis Find period Find key points Plug points in Connect points with smooth line Important Points LT: I can graph sine and cosine curves. Evan Mickelson

Procedure: Using Key Points to Sketch a Sine (or cosine) Curve θ Sketch the graph for y=2sinx on the interval [-π,4π]. STEPS 1. Divide the period by 4 to find key points to graph 1. Gather some points. 2. Plot each point 3. Connect points with a smooth curve, filling the graph to the interval. Remember: y=2sinx=2(sinx) Intercept Maximum Intercept Minimum (0,0) (π/2,2) (3π/2,-2) (2π,0) LT: I can graph sine and cosine curves. Evan Mickelson

Example 1: y=3cosx xfunction y 03cos(0)=3*13 π/2 3cos (π/2) =3*0 0 π 3cos (π )=3*(-1) -3 3 π/2 3cos(3 π/2 )=3*0 0 2π2π 3cos(2 π )=3*1 3 Illustration: Evan Mickelson ™ 2π/4=π/2 LT: I can graph sine and cosine curves. Evan Mickelson

Example 2: y=2+2sinx xfunction y 02+2sin(0)=2+2*02 π/2 2+2sin (π/2) =2+2*1 4 π 2+2sin (π )=2+2*0 2 3 π/2 2+2sin(3 π/2 )=2+2*(-1) 0 2π2π 2+2sin(2 π )=2+2*0 2 Illustration: Evan Mickelson ™ LT: I can graph sine and cosine curves. Evan Mickelson

Common Errors ★ Don't mix up sine and cosine!!! ≠ y=2sinx = y=2cosx LT: I can graph sine and cosine curves. Evan Mickelson

The Classic It's as easy as 1-2-3! Steps to graphing a sine or cosine function Vocab words to remember Interesting thing you learned today LT: I can graph sine and cosine curves. Evan Mickelson