91Ó°ÊÓ

Two pulleys, \(50 \mathrm{cm}\) and \(30 \mathrm{cm}\) in diameter, respectively, are connected by a belt. The larger pulley makes 12 revolutions per minute. Find the angular speed of the smaller pulley, in radians per second. (IMAGE CAN NOT COPY)

Classify the function as linear, quadratic, cubic, quartic, rational, exponential, logarithmic, or trigonometric. $$f(x)=\left(\frac{1}{2}\right)^{x}[5.2]$$

Find the function value. Round to four decimal places. $$\cot 146.15^{\circ}$$

Find the exact acute angle \(\theta\) for the given function value. $$\cos \theta=\frac{\sqrt{3}}{2}$$

A point on the unit circle has \(y\) -coordinate \(-\sqrt{21} / 5\) What is its \(x\) -coordinate? Check using a calculator.

Find the exact acute angle \(\theta\) for the given function value. $$\tan \theta=\sqrt{3}$$

On the earth, one degree of latitude is how many kilometers? how many miles? (Assume that the radius of the earth is \(6400 \mathrm{km},\) or \(4000 \mathrm{mi}\) approximately.)

Find the function value. Round to four decimal places. $$\tan 1086.2^{\circ}$$

At what time between noon and 1: 00 P.M. are the hands of a clock perpendicular?

To find the distance between two points on the earth when their latitude and longitude are known, we can use a right triangle for an excellent approximation if the points are not too far apart. Point \(A\) is at latitude \(38^{\circ} 27^{\prime} 30^{\prime \prime} \mathrm{N},\) longitude \(82^{\circ} 57^{\prime} 15^{\prime \prime} \mathrm{W},\) and point \(B\) is at latitude \(38^{\circ} 28^{\prime} 45^{\prime \prime} \mathrm{N},\) longitude \(82^{\circ} 56^{\prime} 30^{\prime \prime} \mathrm{W}\). Find the distance from \(A\) to \(B\) in nautical miles. (One minute of latitude is one nautical mile.)