Periodic functions

Periodic functions > More trigonometric graphs

Overview

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Exercises

Exercise 1

Determine the function rules for each of these four sinusoids.

Exercise 2

In the previous question more than one answer is possible.

Give at least three for $y_{1}$ .

Use one of these function rules to solve: $y_{1} = -2$ . Round your answer to three decimals.

Exercise 3

The graph of $f$ is a sinusoid. The equilibrium is $y = 1$ , the amplitude is $2$ , the period is $π$ and the graph is increasing in the point $(\frac{1}{6} π, 1)$ .

Create a formula for $f (x)$ .

Use the formula to compute $f (0)$ .

Solve: $f (x) \leq 0$ .

Exercise 4

A ferris wheel has seats $C$ and $D$ . Seat $C$ goes around at a distance of $4$ meters from the axis, seat $D$ at a distance of $8$ meters. The axis of the ferris wheel is elevated $10$ meters from the ground. Study the drawn situation. The ferris wheel goes around once in $8$ seconds. On $t = 0$ seat $D$ is at its highest position. The wheel rotates counterclockwise.

Compute the elevation of the seats $C$ and $D$ when they are in the position given in the drawing .

Determine a function rule for the elevation of seat $D$ .

What is the elevation of seat $C$ at time $t = 1413,25$ ?

For what amount of time during each rotation is seat $C$ elevated more than $12$ m?

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