91Ó°ÊÓ

Find the exact value of the trigonometric function at the given real number. (a) \(\cot \left(-\frac{\pi}{3}\right) \quad\) (b) \(\cot \frac{2 \pi}{3} \quad\) (c) \(\cot \frac{5 \pi}{3}\)

\(17-28\) . Find the amplitude and period of the function, and sketch its graph. $$ y=-\sin 2 x $$

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time \(t=0\) . amplitude 6.25 in, frequency 60 \(\mathrm{Hz}\)

15-20 \(\mathbf{m}\) The point \(P\) is on the unit circle. Find \(P(x, y)\) from the given information. The \(x\) -coordinate of \(P\) is positive, and the \(y\) -coordinate of \(P\) is \(-\sqrt{5} / 5 .\)

Find the period and graph the function. $$ y=-3 \sec x $$

\(11-22\) . Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. \(\tan ^{-1}(-26)\)

\(11-22\) . Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. \(\tan ^{-1}(1.23456)\)

\(17-28\) . Find the amplitude and period of the function, and sketch its graph. $$ y=-3 \sin 3 x $$

15-20 \(\mathbf{m}\) The point \(P\) is on the unit circle. Find \(P(x, y)\) from the given information. The \(x\) -coordinate of \(P\) is \(-\sqrt{2} / 3,\) and \(P\) lies below the \(x\) -axis.

Find the period and graph the function. $$ y=\tan \left(x+\frac{\pi}{2}\right) $$