91Ó°ÊÓ

The equation of simple harmonic motion of a spring/mass system is \(y(t)=\frac{5}{2} \sin (2 t-\pi / 3)\). Determine the initial displacement \(y_{0}\) and initial velocity \(v_{0}\) of the mass.

In Problems \(1-16\), draw the given angle in standard position. Bear in mind that the lack of a degree symbol \(\left(^{\circ}\right)\) in an angular measurement indicates that the angle is measured in radians. $$ 3 $$

Use a sum or difference formula to find the exact value of the given trigonometric function. Do not use a calculator. $$ \tan 165^{\circ} $$

Find the indicated value without the use of a calculator. $$ \sec \left(-120^{\circ}\right) $$

Find the exact value of the given trigonometric expression. Do not use a calculator. $$ \sin \left(\cos ^{-1} \frac{3}{5}\right) $$

Reduce the given expression to a single trigonometric function. $$ \sin x+\cos x \cot x $$

For the given value of \(t\) determine the reference angle \(t^{\prime}\) and the exact values of \(\sin t\) and \(\cos t\). Do not use a calculator. $$ t=2 \pi / 3 $$

Find all solutions of the given trigonometric equation if \(\theta\) represents an angle measured in degrees. $$ 1+\cot \theta=0 $$

Find the indicated value without the use of a calculator. $$ \tan 405^{\circ} $$

Reduce the given expression to a single trigonometric function. $$ \sin \theta \tan \theta \csc ^{2} \theta-\sin \theta \tan \theta $$