91Ó°ÊÓ

Solve the given problems. Display the graphs of \(y=2 \sin 3 x\) and \(y=2 \sin (-3 x)\) on a calculator. What conclusion do you draw from the graphs?

Solve the given problems. Display the graphs of \(y=2 \cos 3 x\) and \(y=\cos (-3 x)\) on a calculator. What conclusion do you draw from the graphs?

Solve the given problems. By noting the periods of \(\sin 2 x\) and \(\sin 3 x,\) find the minimum period of the function \(y=\sin 2 x+\sin 3 x\)

Solve the given problems. By noting the period of \(\cos \frac{1}{2} x\) and \(\cos \frac{1}{3} x,\) find the minimum period of the function \(y=\cos \frac{1}{2} x+\cos \frac{1}{3} x\)

Solve the given problems. Find the function and graph it for a function of the form \(y=-2 \sin b x\) that passes through \((\pi / 4,-2)\) and for which \(b\) has the smallest possible positive value.

Solve the given problems. Find the function and graph it for a function of the form \(y=2 \sin b x\) that passes through \((\pi / 6,2)\) and for which \(b\) has the smallest possible positive value.

Solve the given problems. Find the function and graph it for a function of the form \(y=2 \cos b x\) that passes through \((\pi, 0)\) and for which \(b\) has the smallest possible positive value.

Solve the given problems. Find the function and graph it for a function of the form \(y=-2 \cos b x\) that passes through \((\pi / 2,2)\) and for which \(b\) has the smallest possible positive value.

Solve the given problems. The standard electric voltage in a \(60-\mathrm{Hz}\) alternating-current circuit is given by \(V=170 \sin 120 \pi t,\) where \(t\) is the time in seconds. Sketch the graph of \(V\) as a function of \(t\) for \(0 \leq t \leq 0.05 \mathrm{s}\)

Solve the given problems. To tune the instruments of an orchestra before a concert, an A note is struck on a piano. The piano wire vibrates with a displacement \(y\) (in \(\mathrm{mm}\) ) given by \(y=3.20 \cos 880 \pi t,\) where \(t\) is in seconds. Sketch the graph of \(y\) vs. \(t\) for \(0 \leq t \leq 0.01 \mathrm{s}\)