Math 3 MULTIPLE CHOICE. Choose the one alternative that ...

1 math 3 Final Exam ReviewMULTIPLE choice . Choose the one alternative that best completes the statement or answers the a coterminal angle to find the exact value of the expression. Do not use a )cot7 31)A)1B)3C)32D)33 Find the exact value of the indicated trigonometric function of .2)sec =92 , in quadrant IVFind tan .2)A)-77B)-92C)-772D)-7793)cos =817,3 2< < 2 Find cot .3)A)-83B)178C)-158D)-815 Use the reference angle to find the exact value of the expression. Do not use a )sin-2 34)A)-12B)32C)-1D)-32 Solve the )For what numbers is f( )=cot not defined?

2 5)A)integral multiples of (180 )B)odd multiples of 2 (90 )C)all real numbersD)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 )cos10 36)A)12B)-32C)32D)-12 Use the reference angle to find the exact value of the expression. Do not use a )cot-5 67)A)-33B)3C)33D)-31 Use the even-odd properties to find the exact value of the expression. Do not use a )cos- 48)A)32B)-32C)22D)-22 Use transformations to graph the )y=-2 sin (x+ 3)9)A)B)C)D)210)y=2 cos ( - x)10)A)B)C)D)3 Match the given function to its )1) y= sin x2) y= cos x3) y=-sin x4) y=-cos xABCD11)A)1B, 2D, 3C, 4AB)1A, 2B, 3C, 4DC)1C, 2A, 3B, 4DD)1A, 2D, 3C, 4 BGraph the )y=-3 cot (2x)12)4A)B)C)D)Find the exact value of the )cos-13213)A) 4B) 6C) 4D)11 614)sin-1 ( )14)A) 6B) 6C) 3D)7 3 Use the even-odd properties to find the exact value of the expression.

3 Do not use a )sin (-60 )15)A)32B)-12C)12D)-32 Find the exact value of the )tan-1 (-1)16)A)7 4B) 4C)5 4D)- 4517)cossin-11217)A)32B)22C)1D)0 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the the )csc u- sin u= cos u cot u18)19)cos x csc x tan x= 119)20)sec4 x-tan4 x=sec2 x+tan2 x20) MULTIPLE choice . Choose the one alternative that best completes the statement or answers the the exact value of the expression. Do not use a )sin-1sin4 521)A)54 B) 5C)4 5D)5 Find the exact value of the )tan(cos-1 1)22)A)-1B)32C)0D)22 SHORT ANSWER.

4 Write the word or phrase that best completes each statement or answers the the )1+ csc xsec x= cos x+ cot x23) MULTIPLE choice . Choose the one alternative that best completes the statement or answers the the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a )cot9 424)A)1B)-1C)3D)33 Solve the equation on the interval 0K < 2 .25)sin2 - cos2 = 025)A) 4,3 4,5 4,7 4B) 4C) 4, 3D) 4, 6626)sin2 = 5(cos + 1)26)A){0}B) 2C)No solutionD){ }Find the exact value of the )sin-11 1227)A)6-24B)2-64C)-6+24D)2+6428)sin245 cos5 - cos245 sin5 28)A)-4912B)32C)-32D)-1229)tan175 - tan55 1+ tan175 tan55 29)A)-12B)-2C)-3D)-33 Use the information given about the angle , 0K K 2 , to find the exact value of the indicated trigonometric )cos =45,3 2< < 2 Find sin(2 ).

5 30)A)-2425B)725C)-725D)242531)sin =-45,3 2< < 2 Find cos(2 ).31)A)725B)-2425C)-725D)242532)tan =125, < < 2 Find sin )A)31313B)21313C)-21313D)-31313 Solve the )A radio transmission tower is100 feet tall. How long should a guy wire be if it is to be attached7feet from the top and is to make an angle of23 with the ground? Give your answer to the nearesttenth of a )A) ftB) ftC) ftD) ft34)A twenty-five foot ladder just reaches the top of a house and forms an angle of with the wallof the house. How tall is the house?

6 Round your answer to the nearest )A) ftB) ftC)19 ftD) ft735)A sailboat leaves port on a bearing of S72 W. After sailing for two hours at 12 knots, the boat turns90 toward the south. After sailing for three hours at 9 knots on this course, what is the bearing tothe ship from port? Round your answer to the nearest .35)A) EB) WC) ED) WSolve the )A=30 , B=40 , a=336)A)C=110 ,b= , c= )C=110 ,b= , c= )C=110 ,b= , c= )C=110 ,b= , c= sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or notriangle at all.

7 Solve any triangle(s) that )a=18, b=12,B=20 37)A)one triangleA= ,C= , c= )two trianglesA1= ,C1= ,c1= orA2= ,C2= ,c2= )one triangleA= ,C= , c= )no triangleSolve the )a= 19, b= 16, c= 1138)A)A= ,B= ,C= B)A= ,B= ,C= C)A= ,B= ,C= D)A= ,B= ,C= Solve the )Island A is 150 miles from island B. A ship captain travels 250 miles from island A and then findsthat he is off course and 160 miles from island B. What angle, in degrees, must he turn through tohead straight for island B? Round the answer to two decimal places.

8 (Hint: Be careful to properlyidentify which angle is the turning angle.)39)A) B) C) D) The polar coordinates of a point are given. Find the rectangular coordinates of the )-3,3 440)A)322,-322B)322,322C)-322,322D)-322, -322 The rectangular coordinates of a point are given. Find polar coordinates for the )(-5,5)41)A)52,- 4B)52, 4C)-52, 4D)-52,- 4 Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if )-3i42)A)3(cos180 + i sin180 )B)3(cos0 + i sin0 )C)3(cos90 + i sin90 )D)3(cos270 + i sin270 )843)-6- 8i43)A)10( + i )B)10( + i )C)10( + i )D)10( + i )Write the expression in the standard form a+ )2(cos 75 + i sin 75 )344)A)-42- 42iB)42+ 42iC)-4- 42iD)42- 42iFind all the complex roots.

9 Leave your answers in polar form with the argument in )The complex fifth roots of-2i45)A)42(cos 54 + i sin 54 ),42(cos 126 + i sin 126 ),42(cos 198 + i sin 198 ),42(cos 270 + i sin270 ),42(cos 342 + i sin 342 )B)52(cos 54 + i sin 54 ),52(cos 126 + i sin 126 ),52(cos 198 + i sin 198 ),52(cos 270 + i sin270 ),52(cos 342 + i sin 342 )C)52(cos 45 + i sin 45 ),52(cos 117 + i sin 117 ),52(cos 189 + i sin 189 ),52(cos 261 + i sin261 ),52(cos 333 + i sin 333 )D)32(cos 54 + i sin 54 ), 32(cos 126 + i sin 126 ), 32(cos 198 + i sin 198 ), 32(cos 270 + i sin270 ),32(cos 342 + i sin 342 )The vector v has initial position P and terminal point Q.

10 Write v in the form ai+ bj; that is, find its position )P= (2,6); Q= (-4,-2)46)A)v=-6i- 8jB)v=6i+ 8jC)v=-8i- 6jD)v=8i+ 6jSolve the )Ifv=3i- 3j, )A)32B)6C)18D)6 Find the quantity if v= 5i- 7j and w= 3i+ )v+w48)A)74+13B)89C)26+13D)39 Find the unit vector having the same direction as )v=-8j49)A)u=-jB)u=-18jC)u=64jD)u=-8j9