Trigonometric and Polar Functions

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 $y=-\sin(x+\pi)$?

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?

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?

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

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 $x=0$?

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

If the graph of the sine function has a period of $\pi$ and an amplitude of 3, what is the smallest positive x-value at which the function first reaches its maximum value?