Chapter 7

Find the smallest nomnegation angle betwoen the vectors \(\mathbf{v}\) and \(\mathbf{w} .\) Round your anstoer to the nearest tenth of a degree. $$\mathbf{v}=\langle 1,3\rangle, \mathbf{w}=\langle-2,0\rangle$$

In Exercises \(7-22,\) sketch the graphs of the polar equations. $$\theta=\frac{\pi}{4}$$

Solew the given triangles. The standard notation for labeling of triangles is used. Round answers to four decimal places. $$a=15, b-18, C=37.5^{\circ}$$

Write each of the given vectors in terms of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\). $$\mathbf{v}=\langle-3.5,4\rangle$$

Find \(r\) for the given complex numbers. $$\sqrt{3}+i$$

Find the smallest nomnegation angle betwoen the vectors \(\mathbf{v}\) and \(\mathbf{w} .\) Round your anstoer to the nearest tenth of a degree. $$\mathbf{v}=\langle 0,-1\rangle, \mathbf{w}=\langle 2,3\rangle$$

In Exercises \(7-22,\) sketch the graphs of the polar equations. $$\theta=\frac{2 \pi}{3}$$

Solew the given triangles. The standard notation for labeling of triangles is used. Round answers to four decimal places. $$b=14, c=20, A=78.4^{\circ}$$

Write each of the given vectors in terms of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\). $$\mathbf{u}=\left\langle\frac{1}{3}, \frac{3}{4}\right\rangle$$

Find \(r\) for the given complex numbers. $$\frac{1}{2}+\frac{3}{4} i$$

Find the smallest nomnegation angle betwoen the vectors \(\mathbf{v}\) and \(\mathbf{w} .\) Round your anstoer to the nearest tenth of a degree. $$\mathbf{v}=(-2,0), \mathbf{w}=\langle 0,3\rangle$$

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

Plot the points, given in polar coordinates, on a polar grid. $$\left(1, \frac{\pi}{2}\right)$$

Solew the given triangles. The standard notation for labeling of triangles is used. Round answers to four decimal places. $$a=5, b=7, c=10$$

Solve the given triangles. The standard notation for labeling of triangles is used. Round all answers to four decimal places. $$A=42^{\circ}, B=64^{\circ}, b=6$$

Write each of the given vectors in terms of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\). $$\mathbf{w}=\left\langle-\frac{2}{5}, \frac{1}{6}\right\rangle$$

Find the smallest nomnegation angle betwoen the vectors \(\mathbf{v}\) and \(\mathbf{w} .\) Round your anstoer to the nearest tenth of a degree. $$\mathbf{v}=\langle 2,-4\rangle, \mathbf{w}=\langle 6,3\rangle$$

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

Plot the points, given in polar coordinates, on a polar grid. $$(1, \pi)$$

Solve the given triangles. The standard notation for labeling of triangles is used. Round all answers to four decimal places. $$B=65^{\circ}, C=37^{\circ}, a=10$$

Find \(\mathbf{u}-\mathbf{v}, \mathbf{u}+2 \mathbf{v},\) and \(-3 \mathbf{u}+\mathbf{v}\). $$\mathbf{u}=\langle 3,0\rangle, \mathbf{v}=\langle 5,1\rangle$$

Express each complex number in trigonometric form. $$2 i$$

Find the smallest nomnegation angle betwoen the vectors \(\mathbf{v}\) and \(\mathbf{w} .\) Round your anstoer to the nearest tenth of a degree. $$\mathbf{v}=\langle 4,3\rangle, \mathbf{w}=\langle 2,-1\rangle$$

Plot the points, given in polar coordinates, on a polar grid. $$\left(-3, \frac{\pi}{3}\right)$$

Solew the given triangles. The standard notation for labeling of triangles is used. Round answers to four decimal places. $$a-13, b-17, c=29$$

Solve the given triangles. The standard notation for labeling of triangles is used. Round all answers to four decimal places. $$A=110^{\circ}, B=20^{\circ}, c=15$$

Find \(\mathbf{u}-\mathbf{v}, \mathbf{u}+2 \mathbf{v},\) and \(-3 \mathbf{u}+\mathbf{v}\). $$\mathbf{u}=\langle 6,-2\rangle, \mathbf{v}=\langle 3,-1\rangle$$

Find the smallest nomnegation angle betwoen the vectors \(\mathbf{v}\) and \(\mathbf{w} .\) Round your anstoer to the nearest tenth of a degree. $$\mathbf{v}=\langle 2,4\rangle, \mathbf{w}=\langle-3,2\rangle$$

In Exercises \(7-22,\) sketch the graphs of the polar equations. $$r=-3 \sec \theta$$

Plot the points, given in polar coordinates, on a polar grid. $$\left(-2, \frac{\pi}{6}\right)$$

Solew the given triangles. The standard notation for labeling of triangles is used. Round answers to four decimal places. $$a=19, b=15, c=7$$

Solve the given triangles. The standard notation for labeling of triangles is used. Round all answers to four decimal places. $$B=120^{\circ}, C=35^{\circ}, a=12$$

Find \(\mathbf{u}-\mathbf{v}, \mathbf{u}+2 \mathbf{v},\) and \(-3 \mathbf{u}+\mathbf{v}\). $$\mathbf{u}=\langle-4,5\rangle, \mathbf{v}=\langle 3,-7\rangle$$

Find the smallest nomnegation angle betwoen the vectors \(\mathbf{v}\) and \(\mathbf{w} .\) Round your anstoer to the nearest tenth of a degree. $$\mathbf{v}=\left\langle\frac{1}{3}, 1\right\rangle, \mathbf{w}=\langle 6,-1\rangle$$

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

Plot the points, given in polar coordinates, on a polar grid. $$\left(\frac{1}{2},-\pi\right)$$

Solew the given triangles. The standard notation for labeling of triangles is used. Round answers to four decimal places. $$a=4.7, b=8.4, c=5.6$$

Solve the given triangles. The standard notation for labeling of triangles is used. Round all answers to four decimal places. $$A=80^{\circ}, B=60^{\circ}, a=13$$

Find \(\mathbf{u}-\mathbf{v}, \mathbf{u}+2 \mathbf{v},\) and \(-3 \mathbf{u}+\mathbf{v}\). $$\mathbf{u}=\langle-2,6\rangle, \mathbf{v}=\langle 7,-3\rangle$$

Express each complex number in trigonometric form. $$-5 i$$

Find the smallest nomnegation angle betwoen the vectors \(\mathbf{v}\) and \(\mathbf{w} .\) Round your anstoer to the nearest tenth of a degree. $$\mathbf{v}=\left\langle-2, \frac{3}{2}\right\rangle, \mathbf{w}=\langle 1,2\rangle$$

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

Plot the points, given in polar coordinates, on a polar grid. $$\left(\frac{3}{2},-\frac{\pi}{2}\right)$$

Solew the given triangles. The standard notation for labeling of triangles is used. Round answers to four decimal places. $$a=4.7, b=8.4, c=5.6$$

Solve the given triangles. The standard notation for labeling of triangles is used. Round all answers to four decimal places. $$B=75^{\circ}, C=50^{\circ}, b=25$$

Find \(\mathbf{u}-\mathbf{v}, \mathbf{u}+2 \mathbf{v},\) and \(-3 \mathbf{u}+\mathbf{v}\). $$\mathbf{u}=\langle 1.5,2.5\rangle, \mathbf{v}=\langle 0,1\rangle$$

Express each complex number in trigonometric form. $$1-\sqrt{3} i$$

Calculate projev. Then decompose \(\mathbf{v}\) into \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}\) $$\mathbf{v}=\langle 2,-4\rangle, \mathbf{w}=\langle 2,6\rangle$$

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

Plot the points, given in polar coordinates, on a polar grid. $$\left(0, \frac{3 \pi}{2}\right)$$