Math 3 Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Math Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 1) cot 7 1) 1 C) D) Find the exact value of the indicated trigonometric function of. ) sec = 9, in quadrant IV Find tan. ) C) - 77 D) ) cos = 8 17, - 8 < < Find cot. ) 17 8 C) D) Use the reference angle to find the exact value of the expression. Do not use a calculator. ) sin C) -1 D) - ) Solve the problem. 5) For what numbers is f( ) = cot not defined? 5) integral multiples of (180 ) odd multiples of (90 ) C) all real numbers D) odd multiples of (180 ) Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 6) cos 10 6) 1 - C) D) - 1 Use the reference angle to find the exact value of the expression. Do not use a calculator. 7) cot C) D) - 7) 1

2 Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 8) cos - 8) - C) D) - Use transformations to graph the function. 9) y = - sin (x + ) 9) C) D)

3 10) y = cos ( - x) 10) C) D)

4 Match the given function to its graph. 11) 1) y = sin x ) y = cos x ) y = -sin x ) y = -cos x A B 11) C D 1B, D, C, A 1A, B, C, D C) 1C, A, B, D D) 1A, D, C, B Graph the function. 1) y = - cot (x) 1)

5 C) D) Find the exact value of the expression. 1) cos-1 1) 6 C) D) ) sin-1 (0.5) 1) 6 6 C) D) 7 Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 15) sin (-60 ) 15) - 1 C) 1 D) - Find the exact value of the expression. 16) tan-1 (-1) 16) 7 C) 5 D) - 5

6 17) cos sin ) C) 1 D) 0 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Establish the identity. 18) csc u - sin u = cos u cot u 18) 19) cos x csc x tan x = 1 19) 0) sec x - tan x = sec x + tan x 0) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. Do not use a calculator. 1) sin-1 sin 5 1) 5 5 C) 5 D) 5 Find the exact value of the expression. ) tan(cos-1 1) ) -1 C) 0 D) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Establish the identity. ) 1 + csc x = cos x + cot x ) sec x MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. ) cot 9 ) 1-1 C) D) Solve the equation on the interval 0 <. 5) sin - cos = 0 5),, 5, 7 C), D), 6 6

7 6) sin = 5(cos + 1) 6) {0} C) No solution D) { } Find the exact value of the expression. 7) sin ) C) D) + 6 8) sin 5 cos 5 - cos 5 sin 5 8) C) - D) - 1 9) tan tan tan 175 tan 55 9) C) - D) - Use the information given about the angle, 0, to find the exact value of the indicated trigonometric function. 0) cos = 5, < < Find sin( ). 0) C) D) 5 1) sin = - 5, 7 5 < < Find cos( ). 1) - 5 C) D) 5 ) tan = 1 5, < < Find sin. ) C) D) Solve the problem. ) A radio transmission tower is 100 feet tall. How long should a guy wire be if it is to be attached 7 feet from the top and is to make an angle of with the ground? Give your answer to the nearest tenth of a foot ft ft C) 8.0 ft D) 55.9 ft ) A twenty-five foot ladder just reaches the top of a house and forms an angle of 1.5 with the wall of the house. How tall is the house? Round your answer to the nearest 0.1 foot ft 18.7 ft C) 19 ft D) 18.8 ft ) ) 7

8 5) A sailboat leaves port on a bearing of S7 W. After sailing for two hours at 1 knots, the boat turns 90 toward the south. After sailing for three hours at 9 knots on this course, what is the bearing to the ship from port? Round your answer to the nearest 0.1. N.6 E S.6 W C) N.6 E D) S.6 W 5) Solve the triangle. 6) A = 0, B = 0, a = 6) C = 110, b =.86, c = 5.6 C = 110, b =.86, c = 5.6 C) C = 110, b = 5.6, c =.86 D) C = 110, b = 5.6, c =.86 Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. 7) a = 18, b = 1, B = 0 7) one triangle A = 19.1, C = 10.87, c = 6.6 C) one triangle A = 0.87, C = 19.1, c = 7. two triangles A1 = 0.87, C1 = 19.1, c1 = 7. or A = 19.1, C = 10.87, c = 6.6 D) no triangle Solve the triangle. 8) a = 19, b = 16, c = 11 8) A = 87., B = 5., C = 57. A = 87., B = 57., C = 5. C) A = 57., B = 87., C = 5. D) A = 5., B = 57., C = 87. Solve the problem. 9) Island A is 150 miles from island B. A ship captain travels 50 miles from island A and then finds that he is off course and 160 miles from island B. What angle, in degrees, must he turn through to head straight for island B? Round the answer to two decimal places. (Hint: Be careful to properly identify which angle is the turning angle.) C) D).9 9) The polar coordinates of a point are given. Find the rectangular coordinates of the point. 0) -, 0), -, C) -, D) -, - The rectangular coordinates of a point are given. Find polar coordinates for the point. 1) (-5, 5) 1) 5, - 5, C) -5, D) -5, - Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. ) -i ) (cos i sin 180 ) (cos 0 + i sin 0 ) C) (cos 90 + i sin 90 ) D) (cos 70 + i sin 70 ) 8

9 ) -6-8i ) 10(cos i sin 06.9 ) 10(cos i sin 16.9 ) C) 10(cos i sin 5.1 ) D) 10(cos.1 + i sin.1 ) Write the expression in the standard form a + bi. ) (cos 75 + i sin 75 ) ) - - i + i C) - - i D) - i Find all the complex roots. Leave your answers in polar form with the argument in degrees. 5) The complex fifth roots of -i 5) (cos 5 + i sin 5 ), (cos 16 + i sin 16 ), (cos i sin 198 ), (cos 70 + i sin 70 ), (cos + i sin ) 5 (cos 5 + i sin 5 ), 5 (cos 16 + i sin 16 ), 5 (cos i sin 198 ), 5 (cos 70 + i sin 70 ), 5 (cos + i sin ) C) 5 (cos 5 + i sin 5 ), 5 (cos i sin 117 ), 5 (cos i sin 189 ), 5 (cos 61 + i sin 61 ), 5 (cos + i sin ) D) (cos 5 + i sin 5 ), (cos 16 + i sin 16 ), (cos i sin 198 ), (cos 70 + i sin 70 ), (cos + i sin ) The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. 6) P = (, 6); Q = (-, -) 6) v = -6i - 8j v = 6i + 8j C) v = -8i - 6j D) v = 8i + 6j Solve the problem. 7) If v = i - j, find v. 7) 6 C) 18 D) 6 Find the quantity if v = 5i - 7j and w = i + j. 8) v + w 8) C) D) 9 Find the unit vector having the same direction as v. 9) v = -8j 9) u = -j u = - 1 j C) u = 6j D) u = -8j 8 9