BGSU
4.5 Graphs of Sine and Cosine Functions
Math 1300
The Graph of y = sin x and y = cos x
Example 1 Determine the amplitude of y = 2 sin x. Then graph y = sin x and y = 2 sin x for −π ≤ x ≤
3π.
Exercise 1 Determine the amplitude of y = − 31 cos x. Then grahp y = cos x and y = − 13 cos x for
−3π ≤ x ≤ 3π.
Ying-Ju Tessa Chen
Last modified: October 23, 2014
1
BGSU
4.5 Graphs of Sine and Cosine Functions
The graph of y = A sin(Bx − C), B > 0, has
amplitude = |A|
If C 6= 0, then
C
B
The graph of y = A cos(Bx − C), B > 0, has
amplitude = |A|
2π
.
B
is called the phase shift.
period =
Math 1300
period =
2π
.
B
Example 2 Determine the amplitude, period, and phase shift of each function. The graph one period of
the function.
1. (#24) y = 12 sin(x + π)
2. (#52) y = 3 cos(2πx + 4π)
Example 3 (P.567 Example 9 on the textbook) The figure on P.567 shows that the depth of water at a
boat dock varies with the tides. The depth is 5 feet at low tide and 13 feet at high tide. On a certain day,
low tide occurs at 4 A.M. and high tide at 10 A.M. If y represents the depth of the water, in feet, x hours
after midnight, use a sine function of the form y = A sin(Bx − C) + D to model the water’s depth.
Ying-Ju Tessa Chen
Last modified: October 23, 2014
2