91Ó°ÊÓ

For the following exercises, graph two full periods of each function and state the amplitude, period, and midine. State the maximum and minimum \(y\) -values and their corresponding \(x\) -values on one period for \(x>0 .\) Round answers to two decimal places if necessary. $$ f(x)=2 \cos x $$

For the following exercises, graph two full periods of each function and state the amplitude, period, and midine. State the maximum and minimum \(y\) -values and their corresponding \(x\) -values on one period for \(x>0 .\) Round answers to two decimal places if necessary. $$ f(x)=2 \sin \left(\frac{1}{2} x\right) $$

For the following exercises, graph two full periods of each function and state the amplitude, period, and midine. State the maximum and minimum \(y\) -values and their corresponding \(x\) -values on one period for \(x>0 .\) Round answers to two decimal places if necessary. $$ f(x)=3 \cos \left(\frac{6}{5} x\right) $$

For the following exercises, graph two full periods of each function and state the amplitude, period, and midine. State the maximum and minimum \(y\) -values and their corresponding \(x\) -values on one period for \(x>0 .\) Round answers to two decimal places if necessary. $$ y=5 \sin (5 x+20)-2 $$

For the following exercises, graph one full period of each function, starting at \(x=0 .\) For each function, state the amplitude, period, and midine. State the maximum and minimum \(y\) -values and their corresponding \(x\) -values on one period for \(x>0\) . State the phase shift and vertical translation, if applicable. Round answers to two decimal places if necessary. $$f(t)=2 \sin \left(t-\frac{5 \pi}{6}\right)$$

A video camera is focused on a rocket on a launching pad 2 miles from the camera. The angle of elevation from the ground to the rocket atter \(x\) secondsis \(\frac{\pi}{120} x\) a. Write a function expressing the altitude \(h(x),\) in miles, of the rocket above the ground after \(x\) seconds. Ignore the curvature of the Earth. b. Graph \(h(x)\) on the interval \((0,60)\) . c. Evaluate and interpret the values \(h(0)\) and \(h(30)\) . d. What happens to the values of \(h(x)\) as \(x\) approaches 60 seconds? Interpret the meaning of this in terms of the problem.

Why do the functions \(f(x)=\sin ^{-1} x\) and \(g(x)=\cos ^{-1} x\) have different ranges?

For the following exercises, use a calculator to evaluate each expression. Express answers to the nearest hundredth. $$ \cos ^{-1}(0.8) $$

Graph \(y=\sin ^{-1} x\) and state the domain and range of the function.

Suppose a 13-foot ladder is leaning against a building, reaching to the bottom of a second-floor window 12 feet above the ground. What angle, in radians, does the ladder make with the building?