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 $f^{″}\left(x\right)$?

Use graphing software to graph the functions specified in Exercises 31–36.

Select a viewing window that reveals the key features of the function.

Graph the function f (x) = sin 2x + cos 3x.

Use graphing software to graph the functions specified in Exercises 31–36.

Select a viewing window that reveals the key features of the function.

Graph the function f (x) = sin³ x.

General Sine Curves

For

f(x) = A sin ((2π/B)(x – C) +D

identify A, B, C, and D for the sine functions in Exercises 67–70 and sketch their graphs.

y = ½ sin (πx – x) + ½

General Sine Curves

For

f(x) = A sin ((2π/B)(x – C) +D

identify A, B, C, and D for the sine functions in Exercises 67–70 and sketch their graphs.

y = L/2π sin (2πt/L), L > 0

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.

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

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