91Ó°ÊÓ

Use the unit circle and the fact that sine is an odd function to find each of the following: If \(\cos \theta=-1 / 3\), find \(\cos (-\theta)\).

\(y=1+\sin (2 x-\pi)\)

Graph one complete cycle for each of the following. In each case, label the axes so that the amplitude and period are easy to read. \(y=3 \sin 2 x,-\pi \leq x \leq 2 \pi\)

Use a calculator to evaluate each expression to the nearest tenth of a degree. $$ \arctan (-2.748) $$

Make a diagram of the unit circle with an angle \(\theta\) in QI and its supplement \(180^{\circ}-\theta\) in QII. Label the point on the terminal side of \(\theta\) and the unit circle with \((x, y)\) and the point on the terminal side of \(180^{\circ}-\theta\) and the unit circle with \((-x, y)\). Use the diagram to show that $$ \sin \left(180^{\circ}-\theta\right)=\sin \theta $$

\(y=-1+\sin (2 x+\pi)\)

Use a calculator to evaluate each expression to the nearest tenth of a degree. $$ \arctan (-0.3640) $$

Make a diagram of the unit circle with an angle \(\theta\) in QI and its supplement \(180^{\circ}-\theta\) in QII. Label the point on the terminal side of \(\theta\) and the unit circle with \((x, y)\) and the point on the terminal side of \(180^{\circ}-\theta\) and the unit circle with \((-x, y)\). Use the diagram to show that $$ \cos \left(180^{\circ}-\theta\right)=-\cos \theta $$

Graph one complete cycle for each of the following. In each case, label the axes so that the amplitude and period are easy to read. \(y=-3 \sin 2 x,-2 \pi \leq x \leq 2 \pi\)

\(y=-3+\sin \left(\pi x+\frac{\pi}{2}\right)\)