Determine the value of $y=-2\(\cdot\]\sin\[\left\)(-\(\frac{3\pi}{2}\]\right\))+10$ without using a calculator or the unit circle.

In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = 1/3 sin 2t

In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = −4 sin 3π/2 t

Sketch the function $y=\(\cos\]\left\)(x\(\right\))-1$ on the graph below.

Determine the value of $y=\(\sin\[\left\)(-\(\frac{\pi}{2}\]\right\))+50$ without using a calculator or the unit circle.

Graph the function $y=-3\(\cdot\[\cos\]\left\)(x\(\right\))$.

Given below is the graph of the function $y=\(\sin\]\left\)(bx\(\right\))$. Determine the correct value for b.

The Period for the function $y=\(\cos\]\left\)(bx\(\right\))$ is $T=20\(\pi\)$. Determine the correct value of b.

Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 4 sin x