PreCalc Practice Quiz – Sinusoidal Functions
Graph the following two sinusoidal functions. Please label the 5 key points for one period (the
maximum, minimum, and midline points)
𝜋𝜋
2
𝑦𝑦 = −2 sin �2𝑥𝑥 − � + 1
Amplitude _____
Period ______
Phase Shift ______
Verical Shift ______
𝑥𝑥
𝑦𝑦 = 3 cos � + 𝜋𝜋� − 2
2
Amplitude _____
Period ______
Phase Shift ______
Verical Shift ______
Write a sine and cosine equation for the graph.
Amplitude: _____
Period: _____
Phase shift: sine ____
cosine ____
Vertical shift: ______
Sine equation ______________________________
Write a sine equation with the given information.
Amplitude
Period:
2
3
4
Phase shift: - 3
Vertical shift: 2
cosine equation ___________________________
Write a cosine equation with the given information.
Amplitude: 3
Period: 3π
Phase shift:
𝜋𝜋
3
Reflected over the x axis
Word Problems
For several hundred years, astronomers have kept track of the number of solar flares, or
"sunspots," which occur on the surface of the sun. The number of sunspots counted in a given
year varies periodically from a minimum of about 10 per year to a maximum of about 110 per
year. Maximums occurred in the years 1981, 1992, and 2003.
Write a sine equation expressing the number of sunspots per year in terms of the year starting
at the year 2000. Then write a cosine equation.
Water wheels are still used to power lumber mills in historic recreations. A typical water wheel
makes one complete revolution every 90 seconds. A paddle starts its cycle 1 m below the level
of the water, and reaches a maximum height of 4m above the water. Assume that that the
timing starts when the paddle is at the top of the water wheel.