Sine Cosine Graphs Worksheets Grade 12

1. A cosine function is graphed on a coordinate plane. The function has been transformed from the parent function y = cos(x) by a vertical stretch of factor 2, a horizontal compression such that the period becomes 2π/3, a phase shift of π/6 units to the left, and a vertical translation of 1 unit downward. Write the equation of the transformed function in the form y = a cos(b(x - c)) + d.
2. ∫(3x² - 4x + 2)dx from 0 to 2 = ?
3. A marine biologist is studying the vertical motion of a dolphin swimming near a buoy. The dolphin's depth relative to the surface follows the function d(t) = 4sin(πt/3 - π/2) + 6, where d is depth in meters and t is time in seconds. At what times during the first 6 seconds does the dolphin reach its maximum depth?

…and 4 more problems

1. y = 4sin(2(x - π/3)) + 1. Identify amplitude, period, phase shift, and vertical shift.
2. y = 4sin(2(x - π/3)) + 1. Find amplitude, period, phase shift, and vertical shift.
3. y = 5sin(3(x - π/5)) - 1. Identify amplitude, period, phase shift, and vertical shift.

…and 5 more problems

1. A Ferris wheel at an amusement park has a diameter of 40 meters and completes one full rotation every 2 minutes. The height of a passenger above the ground can be modeled by a transformed cosine function. If the boarding platform is 5 meters above ground level and the wheel rotates counterclockwise, determine the exact height of a passenger 45 seconds after they pass the 3 o'clock position during their ride.
2. y = 8sin(9(x - π/8)) + 7. Identify amplitude, period, phase shift, and vertical shift.
3. A cosine function is graphed on a coordinate plane. The graph shows a wave that has been vertically stretched by a factor of 2, horizontally compressed to have a period of π/2, reflected across the x-axis, shifted π/3 units to the left, and translated 1 unit downward. Write the equation of this transformed cosine function in the form y = a cos(b(x - c)) + d.

…and 4 more problems