Exam 16: Radian Measure, Arc Length, and Circular Motion

What arc length is subtended by a central angle of $108.2^{\circ}$ in a circle of radius $21.2 \mathrm{~cm}$ ?

Evaluate to four significant digits: $\csc 7 \pi / 5$

Evaluate to four significant digits: $\sin^{2} \pi / 3+\tan \pi / 3$

Evaluate to four significant digits: $\cos^{-1} 0.1806$

Convert to radians: 7.40 rev

Convert to revolutions: $3.48 \mathrm{rad}$

Evaluate to four significant digits: $\cot^{-1} 17.1$

Convert to degrees (decimal): $6.30 \mathrm{rad}$

Fill in the missing values.

Convert to degrees (decimal): $3.781 \mathrm{rad}$

Olivia Oliver, an 11-year-old figure skater from Nova Scotia, performed the fastest recorded spin on ice skates on January 19, 2015, turning the equivalent of 342 revolutions per minute. How many degrees would she turn in 12.0 seconds?

Evaluate to four significant digits: $\tan \pi / 9$

One car of a Ferris wheel of radius 25.5 feet goes from the lowest point of its circuit to the highest in 55 seconds. What is the linear speed of the car in mi./h?

A certain town is at a latitude of $24.9^{\circ} \mathrm{S}$ . How far is it from the North Pole? Assume that the earth is a sphere with radius $6370 \mathrm{~km}$ .

Evaluate to four significant digits: $3 \cos \pi / 3+\tan^{2} \pi / 3$