Supplementary Trigonometry Exercise Problems

1 Supplementary Trigonometry Exercise Problems by Professor Yom Trig Section : Angles MULTIPLE the angle as acute, right, obtuse, or )1)A)ObtuseB)StraightC)AcuteD)Right2)2)A )RightB)ObtuseC)StraightD)Acute3)3)A)Rig htB)ObtuseC)StraightD)Acute4)4)A)ObtuseB )RightC)StraightD)AcuteIf possible, find the indicated complement or supplement of the given )66 ;supplement5)A)24 B)204 C)294 D)114 6)118 ;supplement6)A)242 B)62 C)No supplementD)152 7)7 ;complement7)A)83 B)173 C)263 D)353 8)147 ;complement8)A)147 B)No complementC)33 D)57 1 SHORT the measure of the indicated )Two angles of a triangle are 50 and 30 . Find the third )10)Two angles of a triangle are 40 and 70 . Find the third )2 Answer KeyTestname: MATH 06 - TRIG SECTION 01)D2)D3)B4)C5)D6)B7)A8)B9)100 10)70 3 Trig Section :The Trigonometric RatiosMULTIPLE the value of the indicated trigonometric function of the angle in the figure.

2 Give an exact answer with a )710 Find csc .1)A)csc =1497B)csc =7149149C)csc =14910D)csc =101491492)107 Find cot .2)A)105151B)5110C)517D)751513)94 Find cot .3)A)cot =94B)cot =49C)cot =49797D)cot =9979714)65 Find cot .4)A)115B)61111C)51111D)1165)310 Find tan .5)A)tan =103B)tan =1093C)tan =10910D)tan =3106)89 Find tan .6)A)tan =89B)tan =1458C)tan =1459D)tan =987)98 Find cos .7)A)cos =1459B)cos =9145145C)cos =8145145D)cos =14582 Use the given triangles to evaluate the expression. Rationalize all )tan 30 8)A)3B)33C)32D)19)csc 60 9)A)2B)233C)32D)210)tan45 -sin60 10)A)23- 326B)2-22C)-36D)2-3211)cot60 -cos45 11)A)22- 336B)23- 326C)2-32D)2-2212)sec 45 12)A)3B)2C)22D)23313)1 -sin2 30 -sin2 60 13)A)14B)1 -32C)0D)114)1 +cot2 30 -sec2 45 14)A)2B)0C)1D)33 SHORT the definition or identities to find the exact value of the indicated trigonometric function of the acute angle.

3 15)sec =1312 Find csc .15)16)tan =715 Find sin and cos .16)17)cos =265 Find sin and tan .17)18)cot =33 Find sin .18)4 Answer KeyTestname: MATH 06 - TRIG SECTION 11)C2)C3)B4)A5)D6)A7)C8)B9)B10)D11)B12)B 13)C14)A15)13516)sin =78, cos =15817)sin =15, tan =61218)325 Trig Section : Applying Right TrianglesSHORT the )A 29 foot water slide has a 17 foot vertical ladder. How far is it along the ground from theend of the slide back to the base of the ladder that leads to the slide?1)2)A painter leans a 30 foot ladder against one wall of a house. At what height does the laddertouch the wall if the foot of the ladder is 10 ft from the base of the wall?2)3)From a distance of 45 feet from the base of a building, the angle of elevation to the top ofthe building is 68.

4 Estimate the height of the building to the nearest )4)A kite is currently flying at an altitude of 15 meters above the ground. If the angle ofelevation from the ground to the kite is 35 , find the length of the kite string to the )5)From a distance of 1217 feet from a spotlight, the angle of elevation to a cloud base is 43 .Find the height of the cloud base to the nearest )Solve the right triangle using the information given. Round answers to two decimal places, if )b=8, A=30 ; Find a, c, and )7)a=2, A=40 ; Find b, c, and )8)a =7, b =4; Find c, A, and )9)a=4, c =9; Find b, A, and )2 Answer KeyTestname: MATH 06 - TRIG SECTION 21) ft2) ft3)111ft4)26 m5)1135ft6)a= = 7)b= = 8)c = B= 9)b= B= 3 Trig Section : Trigonometric Functions of Any AnglesMULTIPLE the angle in standard )330 1)A)B)C)D)2)60 2)A)B)C)D)13)-150 3)A)B)C)D)24)405 4)A)B)C)D)Find a positive angle less than 360 that is coterminal with the given )-185 5)A)-5 B)185 C)355 D)175 6)548 6)A)274 B)178 C)368 D)188 7)-1031 7)A)671 B)49 C)311 D)131 SHORT a coterminal angle to find the exact value of the expression.

5 Do not use a )cos405 8)39)csc-660 9)10)cot-180 10)MULTIPLE the quadrant in which the angle )sin > 0,cos < 011)A)IB)IIC)IIID)IV12)tan > 0,sin < 012)A)IB)IIC)IIID)IV13)cot < 0,cos > 013)A)IB)IIC)IIID)IVSolve the )Which of the following trigonometric values are negative? (-292 ) (-193 ) (-207 ) 222 14)A)II, III, and IVB)III onlyC)I and IIID)II and IIISHORT the reference angle of the given )122 15)16)-42 16)17)379 17)418)-253 18)19)-517 19)Use the reference angle to find the exact value of the expression. Do not use a )sin 495 20)21)tan 750 21)22)cot 390 22)Find the exact value of the indicated trigonometric function of .23)cos =29, tan < 0 Find sin .23)24)sec =52 , in quadrant IVFind tan .24)25)tan =-103, in quadrant IIFind cos .25)26)cot =-92, cos < 0 Find csc.

6 26)5 Answer KeyTestname: MATH 06 - TRIG SECTION 31)A2)A3)C4)D5)D6)D7)B8)229)23310)undefi ned11)B12)C13)D14)D15)58 16)42 17)19 18)73 19)23 20)2221)3322)323)-77924)-21225)-31091092 6)8526 Trig Section & : Radians and Degrees / ArclengthSHORT the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal )-139 1)2)-480 2)3)6 3)4)12 4)Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal )25)6)26)Convert the angle in radians to )3 7)8) 68)19)6 79)10) 410)Solve the )The minute hand of a clock is 7 inches long. How far does the tip of the minute hand movein 5 minutes? If necessary, round the answer to two decimal )If s denotes the length of the arc of a circle of radius r subtended by a central angle , find the missing )s = meters, = radians, r = ?

7 12)13)r =23 feet, s =14 feet, = ?13)Find the length s. Round the answer to three decimal )s 410yd14)215)s55 3cm15)16)s25 4m16)Solve the )For a circle of radius 4 feet, find the arc length s subtended by a central angle of 60 . Roundto the nearest )18)A pendulum swings though an angle of 30 each second. If the pendulum is 35 inches long,how far does its tip move each second? If necessary, round the answer to two )3 Answer KeyTestname: MATH 06 - TRIG SECTION 4&51) )-8 33) 304) ) 6) 7)540 8)30 9) 10)45 11) ) m13)21 radians14) ) ) ) ft18) Section : Graphing the Trigonometric Functions / Unit Circle MULTIPLE the )What is the domain of the cosine function?1)A)all real numbers, except integral multiples of (180 )B)all real numbersC)all real numbers, except odd multiples of 2 (90 )D)all real numbers from -1 to 1, inclusive2)What is the range of the cosine function?

8 2)A)all real numbers greater than or equal to 0B)all real numbers greater than or equal to 1 or less than or equal to -1C)all real numbers from -1 to 1, inclusiveD)all real numbersSHORT the equation on the interval 0 K < 2 .3)cos x = 03)4)sin x =-14)5)tan x =-15)6)2 cos x -3= 06)7)2 sin x +2= 07)18)2 sin x -1= 08)9)cos - 1 = 09)MULTIPLE the function with its )y = sin x10)A)B)C)D)211) y =3 sin x11)A)B)C)D)312)y =14 sin x12)A)B)C)D)413)y =2 cos x13)A)B)C)D)514)y =12 cos x14)A)B)C)D)SHORT the function using key )y = sin x -215)6 Graph the )y =2 sin x16)17)y =-3 cos x17)18)y =- 2 sin x18)719)y = cos x19)MULTIPLE an equation in the form y = Acos x or y = Asin x that represents the given )20)A)y = 3cos xB)y =-3cos xC)y =-3sin xD)y = 3sin x21)21)A)y = 2cos xB)y =-2cos xC)y =-2sin xD)y = 2sin x822)22)A)y = xB)y = xC)y = xD)y = x9 Answer KeyTestname.

9 MATH 06 - TRIG SECTION 71)B2)C3) 2, 24) 25) 4, 46) 6, 11 67) 4 , 48) 6 , 69)010)C11)B12)A13)B14)C15)16)10 Answer KeyTestname: MATH 06 - TRIG SECTION 717)18)19)20)C21)B22)A11 Trig Section : Trigonometric IdentitiesMULTIPLE the fundamental identities and appropriate algebraic operations to simplify the )cos x (csc x - sec x) - cot x1)A)-1B)1C)0D)cos2x - tan2x2)sin2 x(cot2 x + 1)2)A)1B)cos2 x + 1C)tan2 xD)-13)cos x1 + sin x+ tan x3)A)1B)cos x+ sin xC)sin2xD)sec x4)1 + tan2 xsec x4)A)csc xB)sec xC)-sec xD)15)cos2 xsin2 x+ cos x sec x5)A)csc xB)cot2 xC)csc2 xD)sec2 x6)1 -cos2 x1 +sinx6)A)0B)cot xC)sinxD)tan xSHORT the )tan x(csc x - sin x) = cos x7)8)(1 - cos x)(1 + cos x) =sin2 x8)9)(sec x - tan x)(sec x + tan x) = 19)10)(1 + tan2 x)(1 -sin2x) = 110)11)sec x - 1tan x=tan xsec x + 111)12)1 + sec2 x sin2 x = sec2 x12)1 Answer KeyTestname.

10 MATH 06 - TRIG SECTION 81)A2)A3)D4)B5)C6)C7)tan x(csc x - sin x) = tan x csc x - tan x sin x =sin xcos x 1sin x-sin xcos x sin x =1cos x-sin2 xcos x=1 -sin2 xcos x=cos2 xcos x= cosx8)(1 - cos x)(1 + cos x) = 1 -cos2x =sin2x9)(sec x - tan x)(sec x + tan x) =sec2x -tan2x = 110)(1 +tan2x)(1 -sin2x) =sec2x cos2x =1cos2x cos2x = 111)sec x - 1tan x=sec x - 1tan x sec x + 1sec x + 1=sec2 x - 1tan x(sec x + 1)=tan2 xtan x(sec x + 1)=tan xsec x + 112)1 +sec2 x sin2 x = 1 +sin2 xcos2 x= 1 +tan2 x =sec2