91Ó°ÊÓ

Find the exact value of the trigonometric function at the given real number. (a) \(\cos \left(-\frac{\pi}{6}\right)\) (b) \(\csc \left(-\frac{\pi}{3}\right)\) (c) \(\tan \left(-\frac{\pi}{6}\right)\)

Points on the Unit Circle The point \(P\) is on the unit circle. Find \(P(x, y)\) from the given information. The \(x\) -coordinate of \(P\) is \(\frac{5}{13},\) and the \(y\) -coordinate is negative.

Graph the function. $$g(x)=3+3 \cos x$$

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is zero at time \(t=0\). amplitude 6 in., frequency \(5 / \pi \mathrm{Hz}\)

Find the period, and graph the function. $$y=2 \csc x$$

Points on the Unit Circle The point \(P\) is on the unit circle. Find \(P(x, y)\) from the given information. The \(y\) -coordinate of \(P\) is \(-\frac{3}{5},\) and the \(x\) -coordinate is positive.

Find the exact value of the trigonometric function at the given real number. (a) \(\sin \left(-\frac{\pi}{4}\right)\) (b) \(\sec \left(-\frac{\pi}{4}\right)\) (c) \(\cot \left(-\frac{\pi}{6}\right)\)

Graph the function. $$g(x)=4-2 \sin x$$

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. $$\sin ^{-1}(0.13844)$$

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is zero at time \(t=0\). amplitude 1.2 m, frequency 0.5 Hz