10.8 Vectors  (Page 10/22)

Suppose a body has a force of 3 pounds acting on it to the left, 4 pounds acting on it upward, and 2 pounds acting on it 30° from the horizontal. What single force is needed to produce a state of equilibrium on the body? Draw the vector.

$\beta =\mathrm{50°},a=105,b=45$

$\alpha =\mathrm{43.1°},a=184.2,b=242.8$

Solve the triangle.

Find the area of the triangle.

A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 2.1 km apart, to be 25° and 49°, as shown in [link] . Find the distance of the plane from point $A$ and the elevation of the plane.

Solve the triangle, rounding to the nearest tenth, assuming $\alpha$ is opposite side $a,\beta$ is opposite side $b,$ and $\gamma$ s opposite side $c:a=4, b=6,c=8.$

Solve the triangle in [link] , rounding to the nearest tenth.

Find the area of a triangle with sides of length 8.3, 6.6, and 9.1.

To find the distance between two cities, a satellite calculates the distances and angle shown in [link] (not to scale). Find the distance between the cities. Round answers to the nearest tenth.

Plot the point with polar coordinates $\left(3,\frac{\pi }{6}\right).$

Plot the point with polar coordinates $\left(5,-\frac{2\pi }{3}\right)$

Convert $\left(6,-\frac{3\pi }{4}\right)$ to rectangular coordinates.

Convert $\left(-2,\frac{3\pi }{2}\right)$ to rectangular coordinates.

Convert $\left(7,-2\right)$ to polar coordinates.

Convert $\left(-9,-4\right)$ to polar coordinates.

$x=-2$

$x^2+y^2=64$

$x^2+y^2=-2y$

$r=7\text{cos}\theta$

$r=\frac{-2}{4\cos \theta +\sin \theta }$

$\theta =\frac{3\pi }{4}$

$r=5\sec \theta$

$r=4+4\sin \theta$

$r=7$

Sketch a graph of the polar equation $r=1-5\sin \theta .$ Label the axis intercepts.

Sketch a graph of the polar equation $r=5\sin \left(7\theta \right).$

Sketch a graph of the polar equation $r=3-3\cos \theta$

$-2+6i$

$4-\text{}3i$

$5+9i$

$\frac{1}{2}-\frac{\sqrt{3}}{2}\text{}i$

$z=5\mathrm{cis}\left(\frac{5\pi }{6}\right)$

$z=3\mathrm{cis}\left(\mathrm{40°}\right)$

$z_1=2\mathrm{cis}\left(\mathrm{89°}\right)$

$z_2=5\mathrm{cis}\left(\mathrm{23°}\right)$

$z_1=10\mathrm{cis}\left(\frac{\pi }{6}\right)$

$z_2=6\mathrm{cis}\left(\frac{\pi }{3}\right)$

$z_1=12\mathrm{cis}\left(\mathrm{55°}\right)$

$z_2=3\mathrm{cis}\left(\mathrm{18°}\right)$

$z_1=27\mathrm{cis}\left(\frac{5\pi }{3}\right)$

$z_2=9\mathrm{cis}\left(\frac{\pi }{3}\right)$

Find $z^4$ when $z=2\mathrm{cis}\left(\mathrm{70°}\right)$

Find $z^2$ when $z=5\mathrm{cis}\left(\frac{3\pi }{4}\right)$