91Ó°ÊÓ

Find the magnitude of the horizontal and vertical components of the vector with magnitude 1 pound pointed in a direction of \(8^{\circ}\) above the horizontal. Round to the nearest hundredth.

A boat leaves the marina and sails 6 miles north, then 2 miles northeast. How far from the marina is the boat, and in what direction must it sail to head directly back to the marina?

An airplane is heading north at an airspeed of 500 km/hr, but there is a wind blowing from the northwest at 50 km/hr. How many degrees off course will the plane end up flying, and what is the plane’s speed relative to the ground?

For the following exercises, test each equation for symmetry. Sketch a graph of the polar equation \(r=3-3 \cos \theta\)

For the following exercises, find the powers of each complex number in polar form. Find \(z^{4}\) when \(z=2 \operatorname{cis}\left(70^{\circ}\right)\)

Convert \((2,2)\) to polar coordinates, and then plot the point.

Convert to rectangular form and graph: \(r=-3 \csc \theta\).

Graph \(r=3-5 \sin \theta\).

Plot the complex number \(-5-i\) in the complex plane.