91Ó°ÊÓ

Find the exact radian value. $$\cot ^{-1} 1$$

Find the magnitude and direction of each vector. Find the unit vector in the direction of the given vector. $$\mathbf{v}=\langle 20,-40\rangle$$

Solve each equation, where \(0^{\circ} \leq x<360^{\circ} .\) Round approximate solutions to the nearest tenth of a degree. $$3-5 \sin x=4 \sin x+1$$

A 120 -pound force keeps an 800 pound object from sliding down an inclined ramp. Find the angle of the ramp.

A 25 -pound box is resting on a ramp that is inclined \(9.0^{\circ} .\) Find the magnitude of the normal component of force.

A plane traveling at 180 mph passes 400 feet directly over an observer. The plane is traveling along a straight path with an angle of elevation of \(14^{\circ} .\) Find the distance of the plane from the observer 10 seconds after the plane has passed directly overhead.

A ship leaves a port at a speed of 16 mph at a heading of \(32^{\circ} .\) One hour later another ship leaves the port at a speed of 22 mph at a heading of \(254^{\circ} .\) Find the distance between the ships 4 hours after the first ship leaves the port.

Use a calculator to estimate the value of the trigonometric function. Round to the nearest ten-thousandth. $$\tan (-4.12)$$

A rope is being used to pull a box up a ramp that is inclined at \(15^{\circ} .\) The rope exerts a force of 75 pounds on the box, and it makes an angle of \(30^{\circ}\) with the plane of the ramp. Find the work done in moving the box 12 feet.

Show that the dot product of two nonzero vectors is positive if the angle between the vectors is an acute angle and negative if the angle between the two vectors is an obtuse angle.