Trigonometry Gateway Exam Questions
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1 MATH 1 Trigonometry Fall 00 Circle one: 8:0 / 9: Ms Kracht Trigonometry Gateway Exam Questions Each version of the Gateway Exam will consist of 0 questions Many of the questions on each version of the Gateway will be taken directly from this list; the others will be similar to questions on this list No answer key for this list of problems is available However, your instructor will gladly answer questions about problems you have attempted You are also encouraged to work with other students Calculators will not be permitted on the Gateway Give exact values, simplified where possible Converting Degrees to Radians Convert to radian measure, giving the exact value, simplified Converting Radians to Degrees Convert to degree measure, giving the exact value, simplified 7π rad 7 π 1 rad 8 π 1 rad 9 0π rad π rad Arc Length Find the exact value, simplified, where s is the arc length, r is the radius, and θ is the angle 11 Find s where r = cm and θ = π 1 Find r where s = π cm and θ = π 1 Find θ where r = cm and s = 0π 7 cm 1 Find s where r = cm and θ = π 1 Find r where s = cm and θ = 0π 7 Area of a Sector of a Circle Find the exact value, simplified, where K is the area, r is the radius, and θ is the angle 1 Find K where r = cm and θ = π 17 Find r where K = π cm and θ = π 18 Find θ where r = cm and K = π cm 19 Find K where r = cm and θ = π 0 Find r where K = 0π cm and θ = 0π 7 1
2 1 17π Coterminal Angles I Find the angle between 0 and π radians coterminal with the given angle rad 91π 0 rad 1π 1 rad 1π 0 rad π 8 rad Coterminal Angles II Find the angle between 0 and 0 coterminal with the given angle Definitions of the Trigonometric Functions of a General Angle Find the exact value of the requested trigonometric function of θ if θ is in standard position and P is some point on its terminal side 1 Find sin θ for P, Find cos θ for P, Find tan θ for P 1, Find cot θ for P, Find csc θ for P, Find sec θ for P 8, 7 Find sin θ for P 1, 7 8 Find cos θ for P, 7 9 Find tan θ for P, 0 Find sec θ for P, 9 Unit Circle Definitions of the Trigonometric Functions of a General Angle Find the exact value of the requested trigonometric function of θ if θ is in standard position and P is the intersection of its terminal side with the unit circle that is, P is the terminal point of θ 1 Find sin θ for terminal point P Find cos θ for terminal point P, 1 1, 1 Find tan θ for terminal point P 1, Find cot θ for terminal point P 8 17, Find csc θ for terminal point P, Find sec θ for terminal point P 7, 7 7 Find cos θ for terminal point P 8 Find cot θ for terminal point P 9 Find tan θ for terminal point P 0 Find csc θ for terminal point P 7 8, 1 8 1, 1,,
3 Right Triangle Definitions of the Trigonometric Functions of an Acute Angle Find the exact value of the requested trigonometric function of θ for the given right triangle Not drawn to scale θ c a b 1 Find sin θ for a = and b = Find cos θ for a = and b = 1 Find tan θ for a = 1 and b = 8 Find cot θ for a = 1 and c = Find csc θ for b = and c = Find sec θ for a = 1 and b = 7 Find sin θ for b = and c = 7 8 Find cos θ for b = and c = 7 9 Find tan θ for a = and b = 0 Find sec θ for a = and b = Terminal Points of Special Angles Find the terminal point of the given angle that is, the point of intersection of the unit circle with the terminal side of the angle 1 π rad π rad π rad 7 π rad 9 7π rad sin0 7 sin 7 sin 7 sin 7 cos0 7 cos 0 77 cos Trigonometric Functions of Special Angles I Find the exact value or state undefined π 78 cos 8 csc π 79 cos180 8 csc 80 tan 81 tan 8 tan 8 tan 0 8 csc 87 csc sec 89 sec 90 sec 91 sec0 9 cot 0 9 cot 9 cot 9 cot
4 9 sin π 97 sin 98 sin π 99 sin 11π 0 sin70 1 cos π Trigonometric Functions of Special Angles II Find the exact value or state undefined π cos 9 csc 11π cos 0 cosπ tanπ π tan 7 tan π 8 tan 00 1 csc csc 1π 11 csc π 11 sec π 11 sec π 11 sec 11 sec π 117 cot cot π π 119 cot cot π Reference Angles I Find the reference angle, in radians, for the given angle rad 1 91π 0 rad 1 1π 1 rad 1 1π 0 rad 1 π 8 rad Reference Angles II Find the reference angle, in degrees, for the given angle Reference Angles III Express as a function of a positive, acute angle in degrees 11 sin cos 0 1 tan 1 1 csc 1 sec 1 cot 00 π 17 sin 11π 18 cos Reference Angles IV Express as a function of a positive, acute angle in radians 17π 19 tan csc π 0 π 11 sec 1 cot 11π
5 Negative Angle Identities 1 If sinθ = 1, find sin θ 1 If cosθ =, find cos θ 7 1 If tanθ =, find tan θ 1 1 If cscθ = 1, find csc θ 17 If secθ = 1, find sec θ 18 If cotθ = 97, find cot θ 19 If sin θ = 1, find cos π θ If cos θ = 0, find sin π θ Cofunction Identities 1 If csc θ =, find sec θ 1 If sec θ = 87, find csc π θ 11 If tan θ = 1, find cot π θ 1 If cot θ = 1 0, find tan π θ Pythagorean Identities State the Pythagorean Identity involving the 1 sine function 1 cosine function 17 tangent function 18 cotangent function 19 secant function cosecant function Revised September 1, 00
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