0. Functions

Given the figure showing four curves labeled A, B, C, and D, which represent the functions $f\left(x\right)=\sin x$, $f^{\prime }\left(x\right)$, $f^{″}\left(x\right)$, and $f^{‴}\left(x\right)$, respectively, which curve corresponds to $f^{″}\left(x\right)$?

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

Below is a graph of the function $y=\(\cot\[\left\)(bx+\(\frac{\pi}{2}\]\right\))$. Determine the value of b.

Below is a graph of the function $y=\(\csc\]\left\)(bx\(\right\))$. Determine the value of b.

Below is a graph of the function $y=\(\tan\]\left\)(bx\(\right\))$. Determine the value of b.

Below is a graph of the function $y=\(\sec\[\left\)(bx-\(\pi\]\right\))$. Determine the value of b.

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