Question Type 16: Working with sinusoidal models to calculate values of parameters Exercises

Find the value of $k$ such that the function $y = 5\sin(kx)$ has a frequency of 4.

Compute the value of $y$ when $x = \frac{\pi}{8}$ for $y = 8\cos(4x) + 2$.

Find the amplitude and period of $y = 5\sin(2x) + 3$.

Determine the period of $y = 9\cos(5x) + 11$.

Given $y = A\cos(2x - \frac{\pi}{2}) + 5$, identify the vertical shift and phase shift.

Determine the value of $k$ such that $y = 3\cos\left(kx - \frac{\pi}{3}\right) + 2$ has period 6.

For $y = 4\cos\bigl(3x + \frac{\pi}{6}\bigr) - 1$, find the period and phase shift.

Write a sinusoidal model of the form $y = 3\sin(kx) - 2$ with amplitude 3, period $4\pi$, no phase shift, and vertical shift $-2$. Find $k$.

For $y = 6\sin\bigl(\frac{x}{2} + \frac{\pi}{4}\bigr)$, find the period and angular frequency.

Find the frequency of $y = 7\sin(4x) - 6$.

Find the period of $y = 2\sin\bigl(\frac{\pi x}{3}\bigr) + 1$.

Determine the $x$-coordinate of the first positive peak of $y = 3\cos(2x) + 4$.