Assignment Bonus Chs 6,,8 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. 1) ( 4, ) Find sin t. 1) A) 4 B) 4 C) D) 4 2) If tan =., find the value of tan + tan ( + ) + tan ( + 2 ). 2) A) 11.1 B) 1.1 C) 11.1 + D) undefined Find an equation for the graph. ) ) A) y = cos 1 2 x B) y = cos (2x) C) y = 2 cos 1 x D) y = 2 cos (x) Graph the function. 4) y = sec(2x) 4) 1
A) B) C) D) Find the domain of the function f and of its inverse function f-1. ) f(x) = - cos(10x + ) ) A) Domain of f: (, ) Domain of f-1: (, ) B) Domain of f: (, ) Domain of f-1: [-, ] C) Domain of f: [-, ] Domain of f-1: (, ) D) Domain of f: (, ) Domain of f-1: [-10, 10] Use a calculator to find the value of the expression in radian measure rounded to two decimal places. 6) cot-1-1 6) A) -1.20 B) -21.04 C) -0. D) -68.96 2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Establish the identity. cos x ) sec x - 1 - cos x sec x + 1 = 2 cos x tan2 x ) 8) In 188, the German mathematician and astronomer Friedrich Wilhelm Bessel was the first 8) person to calculate the distance to a star other than the Sun. He accomplished this by first determining the parallax of the star, 61 Cygni, at 0.14 arc seconds (Parallax is the change in position of the star measured against background stars as Earth orbits the Sun. See illustration.) If the distance from Earth to the Sun is about 10,000,000 km and = 0.14 seconds = 0.14 60 minutes = 0.14 60 60 degrees determine the distance d from Earth to 61 Cygni using Bessel's figures. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 9) From the edge of a 1000-foot cliff, the angles of depression to two cars in the valley below are 21 9) and 28. How far apart are the cars? Round your answers to the nearest 0.1 ft. A) 14.4 ft B) 24. ft C) 24.4 ft D) 1.4 ft 10) A photographer points a camera at a window in a nearby building forming an angle of 42 with the 10) camera platform. If the camera is 2 m from the building, how high above the platform is the window, to the nearest hundredth of a meter? A) 1.11 m B) 0.9 m C). m D) 46.82 m
Find the value of the indicated trigonometric function of the angle in the figure. Give an exact answer with a rational denominator. 11) 11) Find csc. 9 A) csc = 9 106 106 B) csc = 106 9 C) csc = 106 D) csc = 106 106 12) 12) 8 Find cot. A) cot = 89 89 B) cot = 8 89 89 C) cot = 8 D) cot = 8 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Establish the identity. 1) cot2x csc x - 1 = 1 + sin x sin x 1) Simplify the trigonometric expression by following the indicated direction. 1 14) Rewrite over a common denominator: 1 - sin + 1 1 + sin 14) Establish the identity. 1) cot 2 x + csc 2 x = 2 csc 2 x - 1 1) 16) ln 1 + sin u + ln 1 - sin u = 2 ln cos u 16) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. 1) cot sin-1 2 2 1) A) 1 B) 2 C) 2 2 D) 2 4
18) cot-1-18) A) 6 B) C) - D) - 6 Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function. 19) g-1 f - 6 19) A) - B) 2 C) 6 D) - 6 Find the exact value of the expression. 20) cot cos-1-2 20) A) - 24 B) - 2 6 C) 2 D) - 24 Find the exact value, if any, of the composite function. If there is no value, say it is "not defined". Do not use a calculator. 21) sin[sin-1(-0.)] 21) A) 0. B) -0. C) 2.8 D) not defined Use a calculator to find the value of the expression rounded to two decimal places. 22) tan-1(-1.) 22) A) -6.1 B) -.69 C) -0.9 D) -0.98 Find the exact solution of the equation. 2) cos-1 x - = cos-1 x 2) A) 0 B) 1 C) - 1 2 D) -1 Find the exact value of the expression. 24) sin-1 0 24) A) 2 B) - 2 C) 0 D) 2) A rotating beacon is located 12 ft from a wall. If the distance from the beacon to the point on the 2) wall where the beacon is aimed is given by a = 12 sec (2 t), where t is in seconds, find a when t = 0.4 seconds. Round your answer to the nearest hundredth. A) 2.6 ft B) -22.40 ft C) 24.91 ft D) 22.40 ft Graph the function.
26) y = csc 1 x 26) A) B) C) D) 6
2) y = cot(4x) 2) A) B) C) D) 28) Find the average rate of change of f(x) = tan x from 0 to 4. 28) A) 4 B) 0 C) 4 D) 1
Match the given function to its graph. 29) 1) y = sin x - 2 2) y = cos x + 2 29) ) y = sin x + 2 4) y = cos x - 2 A B C D A) 1A, 2D, C, 4B B) 1C, 2A, B, 4D C) 1A, 2B, C, 4D D) 1B, 2D, C, 4A Use transformations to graph the function. 0) y = cos x 0) 8
A) B) C) D) 9
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) A mass hangs from a spring which oscillates up and down. The position P of the mass at 1) time t is given by P = 4 cos(4t) What is the amplitude? What is the period? Graph this function over two periods beginning at t = 0. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the sinusoidal function using key points. 2) y = -2 cos 1 2 x + 2 2) 10
A) B) C) D) Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. ) tan 1080 ) A) 1 B) C) 0 D) undefined 4) If cot = -4.2, find the value of cot + cot ( + ) + cot ( + 2 ). 4) A) -12.6 B) -10.6 C) -12.6 + D) undefined Find the exact value of the indicated trigonometric function of. ) csc = -, in quadrant III Find cot. ) 2 A) 2 B) - C) - D) - 2 Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 6) csc (-60 ) 6) A) -2 B) - 2 C) 2 D) 2 11
Find the exact value of the expression if = 4. Do not use a calculator. ) f( ) = cot Find f( ). ) A) -1 B) C) 1 D) 0 Use a calculator to find the approximate value of the expression rounded to two decimal places. 8) cot 10 8) A).08 B) 182.8 C).0 D) 182.4 In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. 9) ( 4, ) Find tan t. 9) 4 A) B) 4 C) D) 4 40) If sin = 0., find sin ( + ). 40) A) 0. B) -0. C) 0. D) -0. 12