91Ó°ÊÓ

Find the linear speed of a point traveling at a constant speed along the circumference of a circle with radius \(r\) and angular speed \(\omega\). $$\omega=\frac{5 \pi \mathrm{rad}}{16 \mathrm{sec}}, r=24 \mathrm{ft}$$

If \(\tan \theta=-\frac{a}{b},\) where \(a\) and \(b\) are positive, and if \(\theta\) lies in quadrant II, find \(\cos \theta\)

Find the distance a point travels along a circle over a time \(t,\) given the angular speed \(\omega\) and radius \(r\) of the circle. Round your answers to three significant digits. $$r=5 \mathrm{cm}, \omega=\frac{\pi \mathrm{rad}}{6 \mathrm{sec}}, t=10 \mathrm{sec}$$

If \(\csc \theta=-\frac{a}{b},\) where \(a\) and \(b\) are positive, and if \(\theta\) lies in quadrant IV, find cot \(\theta\)

If \(\sec \theta=-\frac{a}{b},\) where \(a\) and \(b\) are positive, and if \(\theta\) lies in quadrant III, find tan \(\theta\)

Find the distance a point travels along a circle over a time \(t,\) given the angular speed \(\omega\) and radius \(r\) of the circle. Round your answers to three significant digits. $$r=2 \mathrm{mm}, \omega=6 \pi \frac{\mathrm{rad}}{\mathrm{sec}}, t=11 \mathrm{sec}$$

Use a calculator to evaluate the following expressions. If you get an error, explain why. $$\cos 270^{\circ}$$

Find the distance a point travels along a circle over a time \(t,\) given the angular speed \(\omega\) and radius \(r\) of the circle. Round your answers to three significant digits. $$r=5.2 \text { in., } \omega=\frac{\pi \mathrm{rad}}{15 \mathrm{sec}}, t=10 \mathrm{min}$$

Use a calculator to evaluate the following expressions. If you get an error, explain why. $$\tan 270^{\circ}$$

Find the distance a point travels along a circle over a time \(t,\) given the angular speed \(\omega\) and radius \(r\) of the circle. Round your answers to three significant digits. $$r=3.2 \mathrm{ft}, \omega=\frac{\pi \mathrm{rad}}{4 \mathrm{sec}}, t=3 \mathrm{min}$$