Trigonometry
Worksheet 6.6A
NAME______________________________
State the amplitude, period, and vertical shift for the following graphs. Then write each equation.
1.)
2.)
Which Sinusoidal function is this?______________
Which Sinusoidal function is this?______________
vertical shift: _______ A: _______ Per:__________
Vertical shift: _______ A: _______ Per:_________
Equation __________________
Equation __________________
3.) The depth of water at a beach changes every 12 hours because of the tides. This forms a periodic function. You get
up early on one of the days of spring break and start measuring the depth. The depth at 8 am (t = 0) is 7 feet, which is a
high point. The low at 2 pm is 1 foot deep. Sketch a graph and answer the following.
a) Which sinusoidal function should be used?
b) Find the amplitude of a sinusoidal function that models the tides.
c) Find the vertical shift of a sinusoidal function that models the tides.
d) What is the period of a sinusoidal function that models the tides?
e) Write a sinusoidal function to model the tides.
f) According to your model, determine the height of the tide at 5 P.M.
Trigonometry
Worksheet 6.6A
4.) The average monthly temperatures for the city of Honolulu, Hawaii, are given below. Let January be t = 1.
Jan
73°
Feb
73°
Mar
74°
Apr
76°
May
78°
June
79°
July
81°
Aug
81°
Sep
81°
Oct
80°
Nov
77°
Dec
74°
a) Determine the sinusoidal function that should be used to model the data.
b) Find the amplitude of a sinusoidal function that models the monthly average temperatures.
c) Find the vertical shift of a sinusoidal function that models the monthly average temperatures.
d) What is the period of a sinusoidal function that models the monthly average temperatures?
e) Write a cosine function that models the monthly temperatures.
f) According to your equation, what is the average temperature in August? How does it compare to the actual given
average?
5.) A buoy is floating on the water bobbing up and down a total of 6 feet. From the top of the wave, 3 feet above sea
level, the buoy completes a full cycle every 12 seconds. Write an equation to represent the height of the buoy after t
seconds if at time t = 0, the buoy is at the top of the wave.
Make a sketch
a) What function should you use?
b) What is the amplitude?
c) What is the period?
d) Write an equation
e) Use the equation to estimate the height of the buoy at t = 27 seconds. ________