Graphs of Sine and Cosine Test – Algebra 2 Math (Printable PDF)

Question 1 Features of a sine function (3 points)

For y = −3 sin(4x) + 2, state

1. the amplitude (1 point)
2. the period (1 point)
3. the midline, maximum and minimum (1 point)

Question 2 Phase shift and range (2 points)

For y = 2 cos(x + π/3) − 1, state the phase shift and the range.

Question 3 Equation from a graph (3 points)

The graph shows a cosine function.

Write its equation in the form y = A cos(Bx) + D. (3 points: D, A, B)

Question 4 Write a model (2 points)

Write a cosine function with maximum 11 at x = 0, minimum −3, and period 8.

Question 5 Ferris wheel (3 points)

A Ferris wheel of radius 15 feet has its center 18 feet above the ground and completes one rotation every 30 seconds. The height of a rider who starts at the bottom is h(t) = −15 cos(πt/15) + 18.

1. Find h(0). (1 point)
2. Find h(10). (1 point)
3. When is the rider first at the top? (1 point)

Question 6 Tide depth (2 points)

The depth of water at a dock is d(t) = 2 cos(πt/6) + 7 feet, t in hours after high tide. Find the high-tide depth, the low-tide depth, and the depth at t = 2.

Question 7 Maximum points (2 points)

Find the x-coordinates of all maximum points of y = 4 sin 3x on [0, π].

Question 8 Model from a table (2 points)

A table shows values of a sine-type function: (0, 5), (2, 8), (4, 5), (6, 2), (8, 5). Write an equation of the form y = A sin(Bx) + D.

Question 9 Maximum of a reflected cosine (1 point)

State the maximum value of y = −2 cos x + 3 and the smallest positive x where it occurs.