Sketch the graph of \(y=\cos x\).

Sketch the graph of \(y=\csc x\).

Mini Lecture

1. Graph \(y=\cos x\).

2. Find \(x\) is \(\cos x=-\displaystyle\frac{1}{\sqrt{2}}\) and \(0<x<2\pi\).

3. Give the amplitude and period of the graph of the trigonometric function.

4. Graph \(y=6\sin x\).

5. Graph \(y=\displaystyle\frac{1}{2}\csc x\).

Sketch the graph of \(y=2\sin x\) for \(0\leq x\leq2\pi\).

Sketch one complete cycle of the graph of \(y=\displaystyle\frac{1}{2}\cos x\).

Graph \(y=\sin 2x\) for \(0\leq x\leq 2\pi\).

Graph \(y=\sin 3x\) for \(0\leq x \leq 2\pi\).

Graph one complete cycle of \(y=\cos \left(\displaystyle\frac{1}{2}x\right)\).

Graph \(y=-2\cos x\), from \(x=-2\pi\) to \(x=4\pi\).

Mini Lecture
Graph one complete cycle.

1. \(y=6\sin x\)

2. \(y=\sin 2x\)

3. \(y=\displaystyle\frac{1}{2}\cos 3x\)

4. \(y=-1+\displaystyle\frac{1}{2}\cos 3x\)

Graph \(y=\sin \left(x+\displaystyle\frac{\pi}{2}\right)\), if \(-\displaystyle\frac{\pi}{2}\leq x \leq \displaystyle\frac{3\pi}{2}\).

Mini Lecture

1. \(y=\sin \left(x+\displaystyle\frac{\pi}{4}\right)\)

2. \(y=-\cos \left(2x+\displaystyle\frac{\pi}{2}\right)\)

3. \(y=4\cos \left(2x-\displaystyle\frac{\pi}{2}\right)\)

Find the equation of the line shown in Figure 1.

One cycle of the graph of a trigonometric function is shown in Figure 2. Find an equation to match the graph.

Find an equation of the graph shown in Figure 3.

Find an equation of the graph shown in Figure 4.

Find an equation of the graph shown in Figure 5.

Recall that the diameter of the Ferris wheel used in Chapters 2 and 3 is \(250\) feet and it rotates through one complete revolution every \(20\) minutes. Make a table that shows the rider’s height \(H\) above the ground for each of the nine values of \(t\) shown in Figure 7. Then graph the ordered pairs indicated by the table. Finally, use the graph to find an equation that gives \(H\) as a function of \(t\).

Mini Lecture

1. Find the equation of the line on the graph.

2. Find the equation of the trigonometric function.

3. Find the equation of the trigonometric function.

4. Find the equation of the trigonometric function.

Graph \(y=\displaystyle\frac{1}{3}x-\sin x\) between \(x=0\) and \(x=4\pi\).

Graph \(y=2\sin x+\cos 2x\) for \(x\) between \(0\) and \(4\pi\).

Graph \(y=\cos x+\cos 2x\) for \(0\leq x \leq 4\pi\).

Graph \(y=\sin x+\cos x\) for \(x\) between \(0\) and \(4\pi\).

Mini Lecture
Graph.

1. \(y=1+\sin x\)

2. \(y=3\sin x +\cos 2x\)

Evaluate in radians without using a calculator or tables.

1. \(\sin^{-1}\left(\displaystyle\frac{1}{2}\right)\)

2. \(\arccos\left(-\displaystyle\frac{\sqrt{3}}{2}\right)\)

3. \(\tan^{-1}(-1)\)

Use a calculator to evaluate each expression to the nearest tenth of a degree.

1. \(\arcsin(0.5075)\)

2. \(\arcsin(-0.5075)\)

3. \(\cos^{-1}(0.6428)\)

4. \(\cos^{-1}(-0.6428)\)

5. \(\arctan(4.447)\)

6. \(\arctan(-4.447)\)

Evaluate \(\sin \left(\tan^{-1}\displaystyle\frac{3}{4}\right)\) without using a calculator.

Write the expression \(\sin\left(\cos^{-1}x\right)\) as an equivalent expression in \(x\) only.

Mini Lecture

1. \(\sin^{-1}\left(\displaystyle\frac{\sqrt{3}}{2}\right)\)

2. \(\tan^{-1}(1)\)

3. \(\sin^{-1}\left(-\displaystyle\frac{1}{2}\right)\)

4. \(\tan\left(\sin^{-1}\displaystyle\frac{3}{5}\right)\)

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