Chapter 5

Sketch the graph of each of the given expressions. $$f(x)=\arctan x-\frac{\pi}{2}$$

Graph the given pair of functions on the same set of axes. Are the graphs of \(f\) and \(g\) identical or not? $$f(x)=\cos (x+\pi) ; g(x)=\cos (x)+\cos \pi$$

Find the angle that is complementary to it. $$57^{\circ}$$

Use a scientific calculator to evaluate the giren trigonometric functions to four decimal places. $$\cos 3$$

Use a scientific calculator to evaluate the trigonometric functions. Make sure the calculator is in DEGREE mode. Round to four decimal places. $$\cos 83^{\circ}$$

Graph the given pair of functions in the same window. Graph at least two cycles of each function, and describe the similarities and differences between the graphs. $$f(x)=\tan (3 x) ; f(x)=3 \tan (x)$$

Sketch the graph of each of the given expressions. $$g(x)=\arcsin x+\pi$$

Graph the given pair of functions on the same set of axes. Are the graphs of \(f\) and \(g\) identical or not? $$f(x)=\cos (x+\pi) ; g(x)=-\cos (x)$$

Find the angle that is complementary to it. $$35^{\circ}$$

Use a scientific calculator to evaluate the giren trigonometric functions to four decimal places. $$\sin 1$$

Use a scientific calculator to evaluate the trigonometric functions. Make sure the calculator is in DEGREE mode. Round to four decimal places. $$\sin 78^{\circ}$$

Graph the given pair of functions in the same window. Graph at least two cycles of each function, and describe the similarities and differences between the graphs. $$f(x)=\sec (2 x) ; f(x)=2 \sec (x)$$

Sketch the graph of each of the given expressions. $$f(x)=2 \arccos x$$

Graph the given pair of functions on the same set of axes. Are the graphs of \(f\) and \(g\) identical or not? $$f(x)=\sin (3 x) ; g(x)=\sin \left(\frac{1}{3} x\right)$$

Find the angle that is complementary to it. $$48^{\circ}$$

Use a scientific calculator to evaluate the giren trigonometric functions to four decimal places. $$\sin (-3)$$

Use a scientific calculator to evaluate the trigonometric functions. Make sure the calculator is in DEGREE mode. Round to four decimal places. $$\sec 15^{\circ}$$

Graph the given pair of functions in the same window. Graph at least two cycles of each function, and describe the similarities and differences between the graphs. $$f(x)=\frac{1}{2} \csc (x) ; f(x)=\csc \left(\frac{1}{2} x\right)$$

Sketch the graph of each of the given expressions. $$f(x)=-3 \arcsin x$$

Graph the given pair of functions on the same set of axes. Are the graphs of \(f\) and \(g\) identical or not? $$f(x)=\cos \left(\frac{1}{2} x\right) ; g(x)=\cos (2 x)$$

Find the angle that is complementary to it. $$33^{\circ}$$

Use a scientific calculator to evaluate the giren trigonometric functions to four decimal places. $$\cos (-1.5)$$

Use a scientific calculator to evaluate the trigonometric functions. Make sure the calculator is in DEGREE mode. Round to four decimal places. $$\csc 36^{\circ}$$

Graph the given pair of functions in the same window. Graph at least two cycles of each function, and describe the similarities and differences between the graphs. $$f(x)=\cot (3 \pi x) ; f(x)=\cot \left(\frac{\pi}{3} x\right)$$

Sketch the graph of each of the given expressions. $$g(x)=\arcsin 2 x-\pi$$

Find the angle that is complementary to it. $$15^{\circ}$$

Use a scientific calculator to evaluate the giren trigonometric functions to four decimal places. $$\sin \frac{\pi}{12}$$

Use a scientific calculator to evaluate the trigonometric functions. Make sure the calculator is in DEGREE mode. Round to four decimal places. $$\cot 67^{\circ}$$

Graph the given pair of functions in the same window. Graph at least two cycles of each function, and describe the similarities and differences between the graphs. $$f(x)=\sec \left(\frac{\pi}{2} x\right) ; f(x)=\sec (2 \pi x)$$

Sketch the graph of each of the given expressions. $$g(x)=\arccos \left(\frac{x}{2}\right)+\pi$$

Use a scientific calculator to evaluate the giren trigonometric functions to four decimal places. $$\cos \frac{\pi}{5}$$

Use a scientific calculator to evaluate the trigonometric functions. Make sure the calculator is in DEGREE mode. Round to four decimal places. $$\cot 34^{\circ}$$

The base of a railing for a staircase makes an angle of \(x\) degrees with the horizontal. Let \(d(x)\) be the horizontal distance between the two ends of the base of the railing. If point \(L\) on the railing is 5 feet higher than point \(M,\) find the positive number \(A\) such that \(d(x)=A\) cot \(x .\) Then use your function to find the length of the base of the railing if \(x=35^{\circ}\).

Explain why each of the given expressions is undefined. $$\arccos 4$$

Find the angle that is supplementary to it. $$105^{\circ}$$

Use a scientific calculator to evaluate the giren trigonometric functions to four decimal places. $$\tan 2$$

Find a cofunction that has the same value as the given quantity. $$\sin 35^{\circ}$$

Find the angle that is supplementary to it. $$67^{\circ}$$

Use a scientific calculator to evaluate the giren trigonometric functions to four decimal places. $$\tan (-1)$$

Find a cofunction that has the same value as the given quantity. $$\cos 42^{\circ}$$

Find the angle that is supplementary to it. $$89^{\circ}$$

Use a scientific calculator to evaluate the giren trigonometric functions to four decimal places. $$\tan \frac{3 \pi}{5}$$

Find a cofunction that has the same value as the given quantity. $$\tan 40^{\circ}$$

An angler is standing on the wharf and sees a fish in the water. Let \(l(x)\) be the length of fishing line that would have to be let out in order to catch the fish, where \(x\) (in radians) is the angle of depression of the location of the fish with respect to the tip of the fishing rod. If the horizontal distance of the fish from the tip of the rod is 12 feet, find constants \(A\) and \(C\) such that \(0

Find the angle that is supplementary to it. $$112^{\circ}$$

Use a scientific calculator to evaluate the giren trigonometric functions to four decimal places. $$\cot \frac{5 \pi}{12}$$

Find a cofunction that has the same value as the given quantity. $$\tan 20^{\circ}$$

This set of exercises will draw on the ideas presented in this section and your general math background. What are the domain and range of the function \(f(x)=\csc 2 x+3 ?\)

Find the exact values of the given expressions in radian measure. $$\csc ^{-1} \sqrt{2}$$

Find the angle that is supplementary to it. $$130^{\circ}$$