Exam 4: Trigonometric Functions

State the amplitude, period, phase shift, and vertical translation of the sinusoid. $y=2+6 \sin \left(3 x-\frac{\pi}{4}\right)$

State the amplitude, period, phase shift, and vertical translation of the sinusoid. $y=-3+2 \sin \left(4 x-\frac{\pi}{5}\right)$ Amplitude: ------ Period: ------ Phase shift: ------ Vert. trans.: ------

Which is the correct value of $\sin ^{-1}(0.6) ?$ (Express the answer in radians to the nearest hundredth.)

Sketch one period of the graph of y= sin2x + sin3x.

Which is the correct value of $\cos ^{-1}(0.4)$ (Express the answer in radians to the nearest hundredth.)

For each of the following functions, determine if the graph shows damped oscillation. If so, state the damping factor. (a) $f(x)=4^{-x} \cos 3 x$ (b) $f(x)=x+\cos x$ (c) $f(x)=-5 x \cos 3 x$ (d) $f(x)=4 \sin \frac{x}{3}$ (e) $F(x)=0.45 e^{-0.1 x} \cos 2 x$

State the domain, range, and period of the function $y=\left|\sin ^{3} x\right|$

Find the period and graph the function for $-2 \pi \leq x \leq 2 \pi$ . Be sure to label your graph with the viewing window dimensions. $y=4 \cos 2 x+6 \sin (3 x-2)$

The lengths of the hypotenuse and one leg of a right triangle are 10.5 and 3.7, respectively. Find the measure of the angle opposite the leg whose length is known.

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

For the next 10 years, a small company's business volume can be modeled by the function $f(x)=80(1.03)^{x}+3 \sin \frac{\pi x}{4}$ 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 in 2012? (c) How many years are in each economic cycle for this company?

Jeana sights the top of a building and finds the angle of elevation to be $35^{\circ}$ She moves 100 feet closer and finds that the angle is now $40^{\circ}$ What is the height of the building?

Point $P(-3,5)$ is on the terminal side of $\theta$ . Evaluate the six trigonometric functions for $\theta$ . \theta= ----- \theta= ----- \theta= ----- \theta= ----- \theta= ----- \theta= -----

The wheels on a truck are turning at 550 revolutions per minute as the truck travels at 55 miles per hour. What is the radius, in inches, of the wheels on the truck?

If sin t=0.5299 and cos t=0.8481 , then tan t= ________

$\text { Sketch the graph of } y=2+4 \sin \frac{2}{3} x \text {. }$

The wheel of a train engine turns $315^{\circ}$ as it moves a distance of 4.75 yards. What is the diameter of the wheel of the engine?

Find the period and graph the function for $-2 \pi \leq x \leq 2 \pi$ . Be sure to label your graph with the viewing window dimensions. $y=7 \cos 3 x-3 \sin (2 x-5)$

Find approximate values of $a, b$ , and $h$ (to the nearest hundredth) so that $f(x) \approx a \sin [b(x-h)]$ . $f(x)=4 \sin 3 x-6 \cos 3 x$ a\approx ------- b\approx ------- h\approx -------

The angle of elevation from the top of a building to the top of a nearby taller building is $56.5^{\circ}$ and the angle of depression to the bottom of the taller building is $15.3^{\circ}$ . If the short building is $50.2 \mathrm{~m}$ high, what is the height of the tall building? the tall building?