Chapter 7

find \(\mathbf{v} \cdot \mathbf{w}\) $$\mathbf{v}=\langle-3,4\rangle, \mathbf{w}=\langle 2,-3\rangle$$

Evaluate the given expressions. $$i^{3}$$

Graph each of the given vectors in standard position. $$\langle 1,0\rangle$$

For what value(s) of \(\theta\) in \([0,2 \pi]\) does \(\sin \theta\) reach a maximum value?

Determine the quadrant where the terminal side of each angle lies. $$\theta=-\frac{5 \pi}{4}$$

Use the Law of Cosines to find the umknoten side of each of the given triangles. The standard notation for labeling of triangles is used. Round anstoers to four decimal places. $$a=7, b=10, C=80^{\circ}$$

Complete them to revicw topics relevant to the remaining exercises. Show that \(\sin \left(180^{\circ}-\theta\right)=\sin \theta\).

find \(\mathbf{v} \cdot \mathbf{w}\) $$\mathbf{v}=\langle 6,-1\rangle, \mathbf{w}=\langle 4,3\rangle$$

Evaluate the given expressions. $$(-2 i)^{2}$$

Graph each of the given vectors in standard position. $$\langle 4,-1\rangle$$

For what value(s) of \(\theta\) in \([0,2 \pi]\) does \(\cos \theta\) reach a minimum value?

Determine the quadrant where the terminal side of each angle lies. $$\theta=\frac{11 \pi}{6}$$

Use the Law of Cosines to find the umknoten side of each of the given triangles. The standard notation for labeling of triangles is used. Round anstoers to four decimal places. $$b=8, c=4, A=75^{\circ}$$

Complete them to revicw topics relevant to the remaining exercises. True or False: \(\sin 40^{\circ}=\sin 140^{\circ}\)

Evaluate the given expressions. $$-i^{4}$$

find \(\mathbf{v} \cdot \mathbf{w}\) $$\mathbf{v}=\langle 5,-8\rangle, \mathbf{w}=\left\langle-2, \frac{1}{2}\right\rangle$$

Graph each of the given vectors in standard position. $$\langle -5, -3 \rangle$$

Find \(\theta\) in \([0, \pi]\) such that \(\cos 2 \theta=-1\)

Determine the quadrant where the terminal side of each angle lies. $$\theta=\frac{10 \pi}{3}$$

Use the Law of Cosines to find the umknoten side of each of the given triangles. The standard notation for labeling of triangles is used. Round anstoers to four decimal places. $$a=12, c=8, B=56^{\circ}$$

Find two angles \(\theta, 0<\theta<180\), satisfying the given condition. $$\sin \theta=\frac{1}{2}$$

Graph each of the given vectors in standard position. $$\left\langle 0, \frac{1}{2}\right\rangle$$

Evaluate the given expressions. $$i^{5}$$

find \(\mathbf{v} \cdot \mathbf{w}\) $$\mathbf{v}=\left\langle\frac{3}{2},-1\right\rangle, \mathbf{w}=\langle 4,0\rangle$$

Find \(\theta\) in \([0, \pi]\) such that \(\sin 2 \theta=1\)

Determine the quadrant where the terminal side of each angle lies. $$\theta=-\frac{11 \pi}{6}$$

Use the Law of Cosines to find the umknoten side of each of the given triangles. The standard notation for labeling of triangles is used. Round anstoers to four decimal places. $$a=10, b=5, C=102^{\circ}$$

Find two angles \(\theta, 0<\theta<180\), satisfying the given condition. $$\sin \theta=\frac{\sqrt{3}}{2}$$

Graph each of the given vectors in standard position. $$\left\langle\frac{4}{3},-6\right\rangle$$

Evaluate the given expressions. $$(3+2 i)-(4+i)$$

find \(\mathbf{v} \cdot \mathbf{w}\) $$\mathbf{v}=\langle 3,-1\rangle, \mathbf{w}=\langle 1,3\rangle$$

Find the zero(s) of \(f(\theta)=\cos 2 \theta\) in the interval \([0, \pi]\)

Use the Law of Cosines to find the umknoten side of each of the given triangles. The standard notation for labeling of triangles is used. Round anstoers to four decimal places. $$b=8, c=4, A=75^{\circ}$$

Find two angles \(\theta, 0<\theta<180\), satisfying the given condition. \(\sin \theta=0.8\) (Use a calculator and round to two decimal places.)

Graph each of the given vectors in standard position. $$\langle-2,-5.5\rangle$$

find \(\mathbf{v} \cdot \mathbf{w}\) $$\mathbf{v}=\langle-2,0\rangle, \mathbf{w}=\langle 0,4\rangle$$

Evaluate the given expressions. $$-1-2 i+(5+i)$$

Find the zero(s) of \(f(\theta)=\sin 2 \theta\) in the interval \([0, \pi]\)

Find two angles \(\theta, 0<\theta<180\), satisfying the given condition. \(\sin \theta=0.4\) (Use a calculator and round to two decimal places.)

Write each of the given vectors in terms of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\). $$\mathbf{u}=\langle-4,6\rangle$$

Find \(r\) for the given complex numbers. $$2-i$$

find \(\mathbf{v} \cdot \mathbf{w}\) $$\mathbf{v}=\left\langle-\frac{5}{3}, \frac{4}{5}\right\rangle, \mathbf{w}=\left\langle\frac{2}{5}, \frac{1}{3}\right\rangle$$

In Exercises \(7-22,\) sketch the graphs of the polar equations. $$r=4$$

Solew the given triangles. The standard notation for labeling of triangles is used. Round answers to four decimal places. $$b=10, c=7, A=55^{\circ}$$

Write each of the given vectors in terms of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\). $$\mathbf{v}=\langle 5,-3\rangle$$

Find \(r\) for the given complex numbers. $$3 i$$

find \(\mathbf{v} \cdot \mathbf{w}\) $$\mathbf{v}=\left\langle\frac{6}{5}, \frac{1}{2}\right\rangle, \mathbf{w}=\langle-10,2\rangle$$

In Exercises \(7-22,\) sketch the graphs of the polar equations. $$r=2$$

Solew the given triangles. The standard notation for labeling of triangles is used. Round answers to four decimal places. $$a=20, c=12, B=108^{\circ}$$

Write each of the given vectors in terms of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\). $$\mathbf{w}=\langle-2,-1.5\rangle$$