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What perentage grade should a road have if elevation of the road is 4 degrees? (The percentage grade is defined as the change in the altitude of the road over a 100 -foot horizontal distance. For example a 5\(\%\) grade means that the road rises 5 feet for every 10 feet of horizontal distance.)

Suppose a 15-foot ladder leans against the side of a house so that the angle of elevation of the ladder is 42 degrees. How far is the foot of the ladder from the side of the house?

For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes. $$ f(x)=\tan x-4 $$

For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes. $$ f(x)=2 \tan \left(x-\frac{\pi}{6}\right) $$

For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline. $$ f(x)=\pi \cos (3 x+\pi) $$

For the following exercises, find and graph one period of the periodic function with the given amplitude, period, and phase shift. Sine curve with amplitude \(3,\) period \(\frac{\pi}{3},\) and phase shift \((h, k)=\left(\frac{\pi}{4}, 2\right)\)