No.48

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 . 

—  3. The maximum value is 1 and the minimum value is –1.

—  5. Each function cycles through all the values of the range
 over an x-interval of      .

—  6. The cycle repeats itself indefinitely in both directions of the x-axis.

—  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.