Exam 4: Trigonometric Functions

The angle of elevation from the top of a building to the top of a nearby taller building is $48.3^{\circ}$ and the angle of depression to the bottom of the taller building is $18.1^{\circ}$ If the short building is 61.7m high, what is the height of the tall building?

A guy wire is stretched from the top of a 200 ft transmission tower to a point on the ground 130ft from the center of the base of the tower. What angle, in degrees, does the guy wire make with the ground?

Solve the equation cot x=-3.2 for x in the interval $\pi \leq x \leq 3 \pi$ graphically. Estimate answers to the nearest hundredth.

7 For each of the following functions, determine if the graph shows damped oscillation. If so, state the damping factor. (a) $f(x)=x+\sin x$ (b) $f(x)=3^{-x} \cos 4 x$ (c) $f(x)=-4 x \cos 2 x$ (d) $f(x)=2 \sin 3 x$ (e) $F(x)=0.35 e^{-0.07 x} \cos 2 x$ ch04_p29_35 3/15/10 11:51 AM Page 33 FORM A 4 Chapter Test (continued) NAME

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

Solve the right triangle $\triangle A B C$ for all its unknown parts if $\alpha=43^{\circ}$ and $a=3.5$ .

In the space below, explain how the graph of the function $y=3 \csc \frac{1}{2} x$ is related to a basic trigonometric graph. Determine the period, domain, range, zeros, and asymptotes (if any). Then sketch the graph of the function.

Find the range of the graph of $y=6 \sin \pi x$

Sketch the graph of y= 3sec x for $-\pi \leq x \leq \pi$

Estimate the value of the amplitude graphically of the sinusoidal function $f(x)=3 \sin 3 x+2 \cos 3 x$ .

Find the period of y=3 tan (2x-1) .

Evaluate all six trigonometric functions of the angle $\theta$ . 1. \theta = ---- \theta = ---- \theta = ---- \theta = ---- \theta = ---- \theta = ----

Find the domain of $f(x)=\sin ^{-1}(5 x)$

A certain company that produces a product with seasonal demands projects that monthly sales for the next two years can be modeled by $y=14.25+0.25 x+2.8 \sin \left(\frac{\pi x}{6}\right)$ . In the model, $y$ is the sales in thousands of units and $x$ is the time in months, with $t=1$ representing January, 2006. According to this model, what will be the projected sales for July $2006 ?$

What is the period of y=sin 6 x ?

Which transformation was not performed on y=cos x to obtain $y=-4 \cos \left(2 x+\frac{\pi}{3}\right) ?$

Solve the right triangle $\triangle A B C$ for all its unknown parts if $\beta=38^{\circ}$ and b=4.5

Solve the equation \cot x=2.7 for x in the interval $\pi \leq x \leq 3 \pi$ graphically. Estimate answers to the nearest hundredth.

Which transformation was not performed on y=\sin x to obtain $y=-2 \sin \left(3 x+\frac{\pi}{3}\right) ?$

In the space below, explain how the graph of the function y=-sec 2 x is related to a basic trigonometric graph. Determine the period, domain, range, zeros, and asymptotes (if any). Then sketch the graph of the function.