Sinusoidal Functions

Amplitude, period, midline and phase shift from graphs and contexts: Ferris wheels, tides and daylight.

10 questions, free, marked as you go with a worked explanation on every one.

What this covers

The graph shown is in degrees. What is its amplitude?
The graph shown is in degrees. What is its period, in degrees?
What is the equation of the midline of y = −4 sin(3x) + 7?
Tide height is modelled by h = 1.8 sin((π/6)(t − 3)) + 2.5, with t in hours and the angle in radians. What is the period, in hours?
A Ferris wheel 40 m across has its centre 22 m above the ground and turns once every 2 minutes. A rider starts at the lowest point. Which models the rider's height h, in metres, after t minutes, with angles in radians?
For the Ferris wheel h = 20 sin π(t − 0.5) + 22, angles in radians, what is the rider's height after 0.75 minutes? Give the answer correct to the nearest tenth of a metre.
Daylight in hours is modelled by D = 4.5 sin((2π/365)(t − 80)) + 12.2, where t is the day of the year. What is the greatest number of daylight hours?
Using D = 4.5 sin((2π/365)(t − 80)) + 12.2, with angles in radians, how many hours of daylight are there on day 172? Give the answer correct to the nearest tenth.
The graph shown is in degrees. Which equation could it be?
Water depth at a dock is modelled by y = 3 sin 30(t − 2) + 5, where t is hours after midnight and angles are in degrees. When is the first high tide after midnight?