Trigonometric and Polar Functions

Which equation represents a sinusoidal function with a period of $2\pi$ and an axis of symmetry at $y=5$?

A ferris wheel's height above ground can be modeled as a cosine function where riders start at the lowest point; what are credible parameters for this scenario if its highest point is at least twice its radius above ground?

Given $g(t) = A \cdot \cos(Bt)$, if $B$ is doubled and $A$ remains constant, what happens to the period of $g(t)$?

How does adding phase shift C in transformed function $y= A\cos(Bx-C) + D$ change graph of original cosine function?

What transformation will result in no horizontal change but invert every peak into a trough on the sinusoidal function $y=\cos(x)$?

Assuming that $f(x) = A \sin(B(x-C)) + D$ has a minimum value at $x = C$ what happens if we replace the variable $x$ by the fractional part ${x}$ where ${x}$ denotes the fractional part remaining after removing the integer component from the real number $x$?

If the equation $y = 3 \cdot \sin(2(x - \frac{\pi}{4})) + 1$ represents a sinusoidal function, what is the amplitude of the resulting wave?

If one cycle of a sine curve has an increased period compared to $y = \sin(x)$, what might be true about its transformation?

Given a sinusoidal function used to model daylight hours throughout the year, represented by $y = A \cos(Bt) + C$, what does 'C' primarily represent?

If the sinusoidal function $f(x) = 3 \\sin(2x - \\pi/2) + 4$ represents the height of a Ferris wheel over time, at what height does a passenger start their ride?