91Ó°ÊÓ

Solve each problem. The heading of a helicopter has a bearing of \(240^{\circ} .\) If the 70 -mph wind has a bearing of \(185^{\circ}\) and the air speed of the helicopter is 195 mph, then what are the bearing of the course and the ground speed of the helicopter?

$$\text { Simplify } \frac{\cos (2 x)}{\sin ^{2}(x)}-\csc ^{2}(x)$$

Find a function of the form \(y=A \cos (B(x-C))+D\) that has the same graph as \(y=\sin (2 x-\pi / 4)\)

Solve each problem. A river is \(2000 \mathrm{ft}\) wide and flowing at 6 mph from north to south. A woman in a canoe starts on the eastern shore and heads west at her normal paddling speed of \(2 \mathrm{mph} .\) In what direction (measured clockwise from north) will she actually be traveling? How far downstream from a point directly across the river will she land?

The five key points on one cycle of a sine wave are \((\pi / 3,-1),(2 \pi / 3,-2),(\pi,-3),(4 \pi / 3,-2),\) and \((5 \pi / 3,-1) .\) Find the equation of the wave in the form \(y=A \cos (B(x-C))+D\)

Prove that scalar multiplication is distributive over vector addition, first using the component form and then using a geometric argument.

Prove that vector addition is associative, first using the component form and then using a geometric argument.

Solve the triangle with \(\beta=122.1^{\circ}, a=19.4,\) and \(b=22.6\)

Find all solutions to the equation \(2 \cos (x)+1=0 .\) Use \(k\) to represent any integer.

Find all solutions to the equation \(4 \sin ^{2}(3 x)-3=0\) in the interval \((0, \pi)\)