91Ó°ÊÓ

Given that \(\omega\) is the angular velocity in radians/second of a point on a circle with radius \(r \mathrm{cm},\) express the linear velocity, \(v,\) in \(\mathrm{cm} / \mathrm{second},\) of the point as a function in terms of \(\omega\) and \(r.\)

Specify in which quadrant(s) an angle \(\theta\) in standard position could be given the stated conditions. $$\sin \theta<0 \text { and } \tan \theta>0$$

Solve the equation for the stated solution interval. Find exact solutions when possible, otherwise give solutions to three significant figures. Verify solutions with your GDC. $$2 \sin ^{2} \theta-\sin \theta-1=0,0 \leqslant \theta<2 \pi$$

Solve the equation for the stated solution interval. Find exact solutions when possible, otherwise give solutions to three significant figures. Verify solutions with your GDC. $$\tan ^{2} x-\tan x=2,-90^{\circ} \leqslant x \leqslant 90^{\circ}$$

Solve for \(x\) in the indicated interval. $$2 \cos ^{2} x-3 \sin 2 x=2,0 \leqslant x \leqslant \pi$$

Prove each identity. $$\cot \theta-\tan \theta=2 \cot 2 \theta$$

Specify in which quadrant(s) an angle \(\theta\) in standard position could be given the stated conditions. $$\cos \theta<0 \text { and } \tan \theta<0$$

Solve the equation for the stated solution interval. Find exact solutions when possible, otherwise give solutions to three significant figures. Verify solutions with your GDC. $$3 \cos ^{2} x-6 \cos x=2,-\pi

A circular irrigation system consists of a 400 metre pipe that is rotated around a central pivot point. If the irrigation pipe makes one full revolution around the pivot point in a day, then how much area, in square metres, does it irrigate each hour?

Specify in which quadrant(s) an angle \(\theta\) in standard position could be given the stated conditions. $$\cos \theta>0$$