Exam 4: Trigonometric Functions

From a 75 -foot observation tower, a controller sights a hot-air balloon at an angle of $20^{\circ}$ elevation. If the horizontal distance from the tower to the balloon is 300 feet, how much higher in the air is the balloon?

For the next ten years, a small company's business volume can be modeled by the function $f(x)=68(1.07)^{x}+5 \sin \frac{\pi x}{3}$ where x is the number of years after 2006 and f is the sales in millions of dollars. (a) What are the company's sales in 2006? (b) What does the model predict for sales is 2015 ? (c) How many years are in each economic cycle for this company?

Find an equivalent algebraic expression not involving trig functions for csc $\left(\cos ^{-1} u\right)$ Explain why your expression includes (or does not include) a $\pm$ sign.

Find the amplitude of the graph of $y=3+2 \cos (x-\pi)$

The wheels on a truck are turning at 630 revolutions per minute as the truck travels at 60 miles per hour. What is the radius, in inches, of the wheels on the truck?

Let sin $x=\frac{2}{5} \text { and } \frac{\pi}{2}< x<\pi$ Find tan x

Find an algebraic expression equivalent to $\sec \left(\tan ^{-1} x\right)$

Compute sec 2 .

Find approximate values of a, b , and h (to the nearest hundredth) so that $f(x) \approx a \sin [b(x-h)]+k$ f(x)=2 sin 5x-4 cos 5x