5.6. Phase Shift of Sinusoidal Functions http://www.ck12.org
Example B
Given the following graph, identify equivalent sine and cosine algebraic models.
Solution: Either this is a sine function shifted right byπ 4 or a cosine graph shifted left^54 π.
f(x) =sin(x−π 4 )=cos(x+^54 π)
Example C
Att=5 minutes William steps up 2 feet to sit at the lowest point of the Ferris wheel that has a diameter of 80 feet. A
full hour later he finally is let off the wheel after making only a single revolution. During that hour he wondered
how to model his height over time in a graph and equation.
Solution: Since the period is 60 which works extremely well with the 360◦in a circle, this problem will be shown
in degrees.
TABLE5.8:
Time (minutes) Height (feet)
5 2
20 42
35 82