Highway Grades Complete the table for the values of to four decimal places...

Highway Grades Complete the table for the values of to four decimal places.

(a) How do sin θ, tan θ, and 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 nearest pound, for an 1800-lb car on a stretch of highway that has a grade.