5.6 Inverse trigonometric functions  (Page 8/15)

The line $y=\frac{3}{5}x$ passes through the origin in the x , y -plane. What is the measure of the angle that the line makes with the positive x -axis?

The line $y=\frac{-3}{7}x$ passes through the origin in the x , y -plane. What is the measure of the angle that the line makes with the negative x -axis?

What percentage grade should a road have if the angle of 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 100 feet of horizontal distance.)

A 20-foot ladder leans up against the side of a building so that the foot of the ladder is 10 feet from the base of the building. If specifications call for the ladder's angle of elevation to be between 35 and 45 degrees, does the placement of this ladder satisfy safety specifications?

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?

$f\left(x\right)=-3\cos x+3$

$f\left(x\right)=\frac{1}{4}\sin x$

$f\left(x\right)=3\cos \left(x+\frac{\pi }{6}\right)$

$f\left(x\right)=-2\sin \left(x-\frac{2\pi }{3}\right)$

$f\left(x\right)=3\sin \left(x-\frac{\pi }{4}\right)-4$

$f\left(x\right)=2\left(\cos \left(x-\frac{4\pi }{3}\right)+1\right)$

$f\left(x\right)=6\sin \left(3x-\frac{\pi }{6}\right)-1$

$f\left(x\right)=-100\sin \left(50x-20\right)$

$f\left(x\right)=\tan x-4$

$f\left(x\right)=2\tan \left(x-\frac{\pi }{6}\right)$

$f\left(x\right)=-3\tan \left(4x\right)-2$

$f\left(x\right)=0.2\cos \left(0.1x\right)+0.3$

$f\left(x\right)=\frac{1}{3}\sec x$

$f\left(x\right)=3\cot x$

$f\left(x\right)=4\csc \left(5x\right)$

$f\left(x\right)=8\sec \left(\frac{1}{4}x\right)$

$f\left(x\right)=\frac{2}{3}\csc \left(\frac{1}{2}x\right)$

$f\left(x\right)=-\csc \left(2x+\pi \right)$

What is the largest and smallest population the city may have?

Graph the function on the domain of $\left[0,40\right]$ .