1. Math 120: Elementary Functions
Overview: Sine and Cosine Functions
Review: 16 Point Circle
The graphs of y=sin(x) and y=cos(x)
Properties of y=sin(x) and y=cos(x)
Boxing the “Wave” – the 4 quarters
Sinusoid Functions
amplitude
frequency
mid-line displacement
phase shift
Example: Fitting a sinusoid function to data

2. The 16-Point Unit Circle

3. graphs of sin(x) & cos(x)
Be able to sketch the graphs of the sine and cosine functions and discuss domain & range periodicity (x-intercepts) symmetry relative maximums and minimums intervals of increase & decrease “Boxing the Wave”/the four quarters

4. Boxing the sine function

5. Boxing the cosine and sine functions

6. sinusoid functions
A function is a sinusoid if it can be written in the form where a = amplitude = period c/b = phase shift (from starting point) d = (vertical) displacement from mid-line A function of the form is also a sinusoid

7. Specifics
Given re-write as Example: Graph one period of Graph one period of

8. modeling periodic behavior with sinusoids
Given max/min values M and m, find the mid-line amplitude period starting point (a.k.a. phase shift)

9. Examples
Given the normal monthly temperature in Helena MT, model the temperature as a sinusoid function Max M = 68, min m = 20, period = 12, mid-line displacement = 44, amplitude = 24, phase shift = 4 Ans:
Month 1 2 3 4 5 6 7 8 9 10 11 12
Temp 20 26 35 44 53 61 68 67 56 45 31 21

10. Graph of plus data points