Chapter 2.3, Problem 76E

Complete the table for values of sin θ, tan θ, and $\frac{\pi \theta }{180}$ to four decimal places.

(a) How do sin θ, tan θ, and $\frac{\pi \theta }{180}$ compare for small grades θ?

(b) Highway grades are usually small. Give two approximations of the grade resistance F = W sin θ that do not use the sine function.

(c) A stretch of highway has a 4-ft vertical rise for every 100 ft of horizontal run. Use an approximation from part (b) to estimate the grade resistance, to the nearest pound, for a 2000-lb car on this stretch of highway.

(d) Without evaluating a trigonometric function, estimate the grade resistance, to the nearest pound, for an 1800-lb car on a stretch of highway that has a 3.75° grade.