Trigonometric and Polar Functions

At what value(s) does $\sin(x)=0$ occur in one period of its graph?

If a function has a form of $y = \sin(-x + \frac{3}{2})$, what is its period?

A sinusoidal graph models ocean tides with high tide at noon; if high tide occurs again at midnight, what phase shift should be applied to align its sine model with standard position?

Which transformation corresponds to shifting the graph of $y=\sin(x)$ to obtain $y=-\sin(x+\pi)$?

What phase shift $c$ in radians is introduced in the graph $y = \cos(2x + c)$, if its first positive peak appears at $x=\pi$ instead of $x=0$?

Given a rational function that models the cost per unit produced in a factory, what feature of the graph indicates a production level at which costs are no longer decreasing at the same rate?

What is the period change for the cosine function if given $f(x) = \\cos(3x)$, compared to its parent function $g(x) = \\cos(x)$?

If the period of a cosine function is halved and its amplitude is tripled, what happens to the graph compared to the original cosine function?

What is the period of a basic sine function, y = sin(x)?

If the maximum height of a Ferris wheel is 35 meters and it completes one rotation every 4 minutes, what is the amplitude of the sine function that models the height of a seat over time?