Periodic functions

Periodic functions > Trigonometric graphs and equations

123456Trigonometric graphs and equations

Exercises

Exercise 1

The graphs of the functions below are sinusoids. What are the period and amplitude for each of these? Plot two periods of the graph of each function on your graphing calculator.

$y = 12 \cdot sin (x)$

$h (t) = 50 sin (2 π t) + 10$

$y = 120 cos (\frac{π}{5} \cdot x)$

$P (x) = -20 sin (2 x)$

Exercise 2

Solve the following equations. Approximate in three decimals where necessary.

$5 cos (\frac{1}{2} x + 4) = 1$

$10 sin (\frac{π}{5} (x - 2)) = 5$

$50 cos (4 x) = 25 \sqrt{3}$

$50 - 30 sin (\frac{2 π}{15} x) = 45$

Exercise 3

Given the function $f$ with $f (x) = 20 cos (\frac{π}{4} x) + 10$ on $[0, 16]$ .

Determine the range of $f$ .

Compute all zeroes of the graph of this function.

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

Exercise 4

The elevation of somebody in a ferris wheel can be described by:

$h (t) = 11 + 10 sin (\frac{π}{10} \cdot t)$

waarin $h (t)$ is uitgedrukt in meters en $t$ in seconden.

Plot the graph of $h (t)$ on your graphing calculator.

What do the numbers $11$ and $10$ in the formula mean for the ferris wheel?

After one period the wheel has gone around exactly once. Determine the period in seconds.

Compute for how long the seat of the ferris wheel is more than $18$ meters above the ground.

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