Chapter 1: Trigonometric Functions 1. Find (a) the complement and (b) the supplement of 61. Show all work and / or support your answer.

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1 Trig Exam Review F07 O Brien Trigonometry Exam Review: Chapters,, To adequately prepare for the exam, try to work these review problems using only the trigonometry knowledge which you have internalized and the departmental formula sheet which is attached at the end of this review. No peeking at your notes, homework, text, solutions manual, or other resources. Note: Anytime you are asked to perform a calculation manually or to give an exact answer, you may not use a calculator. Chapter : Trigonometric Functions. Find (a) the complement and (b) the supplement of 6. Show all work. Perform the calculation 8 ' 9" ' " manually. Show all work. Manually convert 7 ' 9" to decimal degrees. Round to the nearest thousandth of a degree. Show all work. Manually convert the angle 6.8 to degrees, minutes, and seconds. Show all work. Find the smallest positive coterminal angle for. Show all work 6. Sketch the angle θ = in standard position. What quadrant does it terminate in? Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with θ. Show all work 7. A tire is rotating 0 times per minute. Through how many degrees does it rotate in 8 seconds? Show all work 8. Find the exact values of the six trigonometric functions for the angle in standard position having the point (, ) its terminal side. Rationalize denominators if applicable. Show all of your work. on y 9. Suppose that the point (x, y) is in quadrant IV. Decide whether the ratio r is positive or negative. Show all work 0. Manually evaluate the expression cot 70 o sec80 o + sin 90 o. Show all work and / or support your. Use the appropriate reciprocal identity to find tan θ, if Show all work cot θ =. Rationalize denominators when applicable.. Identify the quadrant or quadrants for the angle satisfying the condition cos θ < 0, csc θ > 0. Show all of your work.. Give the signs of the sine, cosine, and tangent functions for 7. Show all work. Is the statement sin θ =.6 possible? Explain why it is or is not.. Use identities to find sin θ, if sec θ =, with θ in quadrant IV. Show all work 6. Find all trigonometric function values for the angle θ if tan θ = in Quadrant III. Show all work 7. Use the reciprocal, quotient, and Pythagorean identities to give three expressions that complete the following statement: cot θ =.

2 Trig Exam Review F07 O Brien Chapter : Acute Angles and Right Triangles 8. Match the trigonometric function in the first row with its value in the second row. Do not use a calculator. Show all work a. csc 60 b. cos c. tan 0 A. B. C. D. E. F. 9. ABC is a right triangle with side lengths a = and b = and a 90 angle at C. Find the length of side c and the six trigonometric function values for angle B. Do not use a calculator. Show all work 0. Write csc. in terms of its cofunction. Show all work. Find one solution for the equation sin (θ + 0 ) = cos (θ 0 ). Show all work. Give the exact value of (a) sec and (b) cot 0. Show all work. In the diagram below, find the exact value of each part labeled with a variable. Show all work and / or support your. Match each angle in the first row with its reference angle in the second row. Show all work and / or support your a. 8 b. c. 780 A. 0 B. C. D. 76 E. 60 F.. Find exact values of the six trigonometric functions for: (a) 80 (b) (c) 0. Show all work and / or support your 6. Find all values of θ, if θ is in the interval [0, 60 ) and has the given function value. Show all work and / or support your a. sec θ = b. tan θ = 7. Use a calculator to find a decimal approximation for sec 7 '. Round your answer to four decimal places. Show all work 8. Find a value of θ in the interval [0, 90 ] for which cot θ =.76. Show all work 9. Use a calculator to evaluate cos 00 cos 80 sin 00 sin 80. Show all work 0. A car traveling on a.8 uphill grade has a grade resistance of 6.96 lb. What is the weight of the car? Show all work. Solve the right triangle shown below. Show all work Answers should be shown with the correct number of significant digits.

3 Trig Exam Review F07 O Brien. Solve the right triangle ABC where a = 76. yd, b = 9. yd, and C = 90. Give angles in degrees and minutes. Show all work Answers should be shown with the correct number of significant digits.. An airplane is flying at 0,0 ft above ground level. The angle of depression from the plane to the base of a tree is 7 '. How far must the plane travel horizontally to be directly over the tree? Show all work and / or support your Your answer should be shown with the correct number of significant digits.. The angle of elevation from the top of a small building to the top of a nearby taller building is 6 0', while the angle of depression to the bottom is 0'. If the smaller building is 8.0 m high, find the height of the taller building. Show all work Your answer should be shown with the correct number of significant digits.. Two ships leave port at the same time. The first ship sails on a bearing of 0 at 8 knots (nautical miles per hour) and the second at a bearing of 0 at 6 knots. How far apart are they after. hrs? Show all work and / or support your Your answer should be shown with the correct number of significant digits. 6. The bearing from Elliston to Pangle is N E. The bearing from Pangle to Themster is S 8 E. A car driven at 60 mph takes hr to go from Elliston to Pangle and.8 hr to go from Pangle to Themster. Find the distance from Elliston to Themster. Show all work Your answer should be shown with the correct number of significant digits. 7. An antenna is erected on the roof a building. From a point 8 feet in front of the building, the angle of elevation to the base of the antenna is 67., while the angle of elevation to the top of the antenna is 68.. Find the height of the antenna. Show all work Your answer should be shown with the correct number of significant digits. Chapter : Radian Measure and Circular Functions 8. Convert (a), (b), and (c) 0 ' to radians. Show all work On parts a and b, express your answer in terms of π. On part c, round your answer to three decimal places. 9. Convert (a) π, (b) 7π, and (c) 8.90 to degrees. Show all work π 0. Find the exact value of tan. Do not use a calculator. Show all work 6. Use the arc length formula to find the missing variable. Show all work π π a. θ =, r =, find s. b. s = 6, r =, find θ. c. θ =, s = 6π, find r.. Find the distance in kilometers between Halifax, Nova Scotia, N, and Buenos Aires, Argentina, S. Show all work [Hint: The radius of the earth is about 600 km.] Your answer should be shown with the correct number of significant digits.. Find the radius of a pulley if a rotation of.6 raises the weight. cm. Show all work and / or support your Your answer should be shown with the correct number of significant digits.. A small gear and a large gear are meshed. An 80.0 rotation of the smaller gear causes the larger gear to rotate 0.0. Find the radius of the larger gear if the smaller gear has a radius of.7 cm. Show all work and / or support your. Find the area of a sector of a circle having radius r = 90.0 km and central angle θ = 70. Show all work and / or support your

4 Trig Exam Review F07 O Brien 6. Find the exact values of (a) sin θ, (b) cos θ. and (c) tan θ for θ = π. Do not use a calculator. Show all work 7. Find the exact circular function value for (a) tan 7π π, (b) csc. Show all work 6 8. Find a calculator approximation for cot (-8.9). Show all work 9. Find the value of t in the interval [0, π ] such that csc t =.09. Show all work 0. Find the value of t in the given interval that has the given circular function value. Do not use a calculator. Show all work π π a., π ; cos t = b. π, ; tan t = π c., π ; sin t =. π Suppose that point P is on a circle with radius 0 cm, and ray OP is rotating with angular speed radians per second. a. Find the angle generated by P in 6 sec. Show all work 8 b. Find the distance traveled by P along the circle in 6 sec. Show all work c. Find the linear speed of P. Show all work π. Given ω = radians per sec and t = sec, use the formula for angular speed to find θ. Show all work and / or support your. Given v = 9 m per sec and r = m, use the formula for linear speed to find ω. Show all work and / or support your. Given s = 6π π yd, r = 9 yd, and ω = radians per second, use the formulas for arc length and angular speed to find t. Show all work. The tires of a bicycle have radius in. and are turning at the rate of 00 rpm. How fast is the bicycle traveling in mph? Show all work [Hint: 80 ft = mile.]

5 Trig Exam Review F07 O Brien Answers Chapter : Trigonometric Functions. 9 ; ' 8" II. 6 ' 9". sin θ is positive; cos θ and tan θ are negative. 06. not possible 6. III; 9 ; ,60 6. sin θ = 8. sin θ = cos θ = csc θ = - sec θ = tan θ = cot θ = 7. cos θ = tan θ = csc θ = sec θ = - cot θ = tan θ ; cos θ sin θ ; ± ( csc θ ) 9. y will be negative because y is negative in Q IV and r is always positive. r Chapter : Acute Angles and Right Triangles 8. E; B; A 6. ; ; 60 ; 0 9. c = sin B = cos B = tan B = csc B = sec B = cot B = sec lbs. θ= ; ; 98. ;. 8.9; 6 0'; 7 0'. a = ; b = d = ; c = 6. 9,0 ft. D; C; E. 6 m a. sin 80 = cos 80 = tan 80 =. 7 nautical miles csc 80 = b. sin (- ) = sec 80 = - cot 80 = cos (- ) = 6. 0 miles tan (- ) = ft csc (- ) = sec (- ) = cot (- ) = c. sin 0 = cos 0 = csc 0 = - sec 0 = tan 0 = cot 0 =

6 Trig Exam Review F07 O Brien Chapter : Radian Measure and Circular Functions 8. π π ; ;.0 7. ; ; ; π;.; 8 0. π 7π 7π ; ; km. π ;.6 cm;.97 cm per sec..7 cm. π. 8.7 cm. 9 rad per sec km. sec 6. ; 0; undefined.. mph 6

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