91Ó°ÊÓ

\(23-44=\) Find the exact value of the expression, if it is defined. \(\cos ^{-1}\left(\cos \left(\frac{17 \pi}{6}\right)\right)\)

Find the period and graph the function. $$ y=2 \tan 3 \pi x $$

\(29-42\) . Find the amplitude, period, and phase shift of the function, and graph one complete period. $$ y=5 \cos \left(3 x-\frac{\pi}{4}\right) $$

The terminal point \(P(x, y)\) determined by a real number \(t\) is given. Find \(\sin t, \cos t,\) and \(\tan t\). \(\left(-\frac{5}{13},-\frac{12}{13}\right)\)

\(23-44=\) Find the exact value of the expression, if it is defined. \(\tan ^{-1}\left(\tan \left(\frac{4 \pi}{3}\right)\right)\)

Find the period and graph the function. $$ y=2 \tan \frac{\pi}{2} x $$

\(29-42\) . Find the amplitude, period, and phase shift of the function, and graph one complete period. $$ y=2 \sin \left(\frac{2}{3} x-\frac{\pi}{6}\right) $$

Spring-Mass System The frequency of oscillation of an object suspended on a spring depends on the stiffness \(k\) of the spring (called the spring constant) and the mass \(m\) of the object. If the spring is compressed a distance \(a\) and then allowed to oscillate, its displacement is given by $$ f(t)=a \cos \sqrt{k / m} t $$ (a) A 10 -g mass is suspended from a spring with stiffness \(k=3 .\) If the spring is compressed a distance 5 \(\mathrm{cm}\) and then released, find the equation that describes the oscillation of the spring. (b) Find a general formula for the frequency (in terms of \(k\) and \(m ) .\) (c) How is the frequency affected if the mass is increased? Is the oscillation faster or slower? (d) How is the frequency affected if a stiffer spring is used (larger \(k\) )? Is the oscillation faster or slower?

The terminal point \(P(x, y)\) determined by a real number \(t\) is given. Find \(\sin t, \cos t,\) and \(\tan t\). \(\left(\frac{\sqrt{5}}{5}, \frac{2 \sqrt{5}}{5}\right)\)

Find the period and graph the function. $$ y=5 \csc \frac{3 \pi}{2} x $$