91Ó°ÊÓ

In Exercises 93-96, find the radian measure of the central angle of a circle of radius \(r\) that intercepts an arc of length \(s\). \(Radius\) \(r\) 4 inches \(Arc\) \(Length\) \(s\) 18 inches

SALES A company that produces snowboards, which are seasonal products, forecasts monthly sales over the next 2 years to be \(S = 23.1 + 0.44t + 4.3\ cos(\pi t/6)\), where \(S\) is measured in thousands of units and \(t\) is the time in months, with \(t=1\) representing January 2010. Predict sales for each of the following months. (a) February 2010 (b) February 2011 (c) June 2010 (d) June 2011

In Exercises 99-104, fill in the blank. If not possible, state the reason. (Note: The notation \(x\rightarrow c^{+}\) indicates that \(x\) approaches \(c\) from the right and \(x\rightarrow c^{-}\) indicates that \(x\) approaches \(c\) from the left.) As \(x\rightarrow \infty\), the value of arctan \(x\rightarrow\) _________.

ELECTRIC HOIST An electric hoist is being used to lift a beam (see figure). The diameter of the drum on the hoist is 10 inches, and the beam must be raised 2 feet. Find the number of degrees through which the drum must rotate.

LINEAR AND ANGULAR SPEEDS A circular power saw has a \(7\frac{1}{4}\)-inch- diameter blade that rotates at 5000 revolutions per minute. (a) Find the angular speed of the saw blade in radians per minute. (b) Find the linear speed (in feet per minute) of one of the 24 cutting teeth as they contact the wood being cut.

Define the inverse secant function by restricting the domain of the secant function to the intervals \([0, \pi/2)\) and \((\pi/2, \pi]\), and sketch its graph.

Define the inverse cosecant function by restricting the domain of the cosecant function to the intervals \([-\pi/2, 0)\) and \((0, \pi/2]\), and sketch its graph.

SPEED OF A BICYCLE The radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the figure are 4 inches, 2 inches, and 14 inches, respectively. A cyclist is pedaling at a rate of 1 revolution per second. (a) Find the speed of the bicycle in feet per second and miles per hour. (b) Use your result from part (a) to write a function for the distance \(d\) (in miles) a cyclist travels in terms of the number \(n\) of revolutions of the pedal sprocket. (c) Write a function for the distance \(d\) (in miles) a cyclist travels in terms of the time \(t\) (in seconds). Compare this function with the \(t\) function from part (b). (d) Classify the types of functions you found in parts(b) and (c). Explain your reasoning.

THINK ABOUT IT A fan motor turns at a given angular speed. How does the speed of the tips of the blades change if a fan of greater diameter is installed on the motor? Explain.