Review: 4.5-Graphs of sine and cosine functions

Properties of sine and cosine functions
1. The domain is the set of real numbers.
2. The range is the set of y values such that −1≤ y ≤1
3. The maximum value is 1 and the minimum value is –1.
5. Each function cycles through all the values of the range 2π over an x-interval of 2π
6. The cycle repeats itself indefinitely in both directions of the x-axis.

The standard equations for sine and cosine are:

y = a sin b (x - c)
y = a cos b (x – c)

• |a| is the amplitude of the sine or cosine graph. 
• The amplitude describes the height of the graph.
• “b” affects the period of the sine or cosine graph. 
• “c” indicates the phase shift of the sine graph or of the cosine graph. 
• The x-coordinate of the key point is c.

The standard graphs of sine and cosine are: 

Math joke of the day: