91Ó°ÊÓ

Using the same set of axes, graph the pair of equations. \(y=x^{2}\) and \(y=(x-1)^{2}\)

Use a calculator to find the values of the following trigonometric functions. . \(\cot 34^{\circ}\)

Use a calculator to find the degree measure of an acute angle whose trigonometric function is given. \(\sin t=0.45\)

Use a calculator to find the degree measure of an acute angle whose trigonometric function is given. \(\cos t=0.72\)

Use a calculator to find the degree measure of an acute angle whose trigonometric function is given. \(\tan t=0.84\)

Use a calculator to find the radian measure of an acute angle whose trigonometric function is given. \(\sin t=0.59\)

Sound Waves. The pitch of a sound wave is measured by its frequency. Humans can hear sounds in the range from 20 to \(20,000 \mathrm{~Hz}\), while dogs can hear sounds as high as \(40,000 \mathrm{~Hz}\). The loudness of the sound is determined by the amplitude. \({ }^{22}\). The note A above middle \(C\) on a piano generates a sound modeled by the function \(g(t)=4 \sin (880 \pi t)\), where \(t\) is in seconds. Find the frequency of \(\mathrm{A}\) above middle \(\mathrm{C}\).

The tangent of a road's angle of elevation \(t\) is called the grade of the road; the grade is often expressed as a percentage. Suppose a highway through a mountain pass has a grade of \(5 \%\) and is \(6 \mathrm{mi}\) long from the base to the top of the pass. How much higher is the pass than the base?

Show that \(\cos ^{2} t=(1+\cos 2 t) / 2\)

Graph the following functions on \([-2 \pi, 2 \pi]\). a) \(y=2 \cos 2 t-1\) b) \(y=2 \cos (2[t+\pi / 6])-1\) c) How does the horizontal shift change the graph?