Trigonometry Exam 2 Review: Chapters 4, 5, 6

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1 Trig Exam Review F07 O Brien Trigonometry Exam Review: Chapters,, 0% of the questions on Exam will come from Chapters through. The other 70 7% of the exam will come from Chapters through. There may be some fill-in-the blank, matching, true-false, and/or multiple choice questions, as well as problems you must work out. To prepare for the second exam, I d suggest you do the following:. Go over your notes and the Quick Reviews at the end of every chapter from through.. Go over the Concept Questions in each section from. through... Rework Exam, and work the problems on this review, using only the departmental formula sheet. Try not to peek at your notes, homework, text, solutions manual, or other resources.. Try to finish the review a few days before the exam so you have time to go back through it and make sure you can do all the problems on your own. Directions: On every problem, show all of your support work and / or explain how you came up with your answer. Anytime you are asked to perform a calculation manually or to give an exact answer, you may not use a calculator.. Given y sin ( x - π) + b. Find: amp: x-axis reflection: period: c. Find: key points:. Given y cos x + b. Find: amp: x-axis reflection: period: c. Find: key points:. Given y tan x + a. Find: a b c d b. Find: x-axis reflection: period: c. Find: left asymptote: x right asymptote: x d. Find: left key point: middle key point: right key point: e. Manually graph two periods of the given function.

2 . Given y cot ( x + π) Trig Exam Review F07 O Brien a. Find: a b c d b. Find: x-axis reflection: period: c. Find: left asymptote: x right asymptote: x d. Find: left key point: middle key point: right key point: e. Manually graph two periods of the given function.. Given y csc x - b. Find: amp of sine: x-axis reflection: period: x-increment: phase shift: vertical translation: c. Find: key points of sine. Given y sec ( x + π) + b. Find: amp of cosine: x-axis reflection: period: x-increment: phase shift: vertical translation: c. Find: key points of cosine 7. An object is attached to a coiled spring. It is pulled down a distance of units from its equilibrium position and then released. The time for one complete oscillation is sec. a. Write an equation that models the position of the object at time t. b. Determine the position at t. sec. c. Find the frequency. 8. The height attained by a weight attached to a spring set in motion is s(t) cos 8πt inches after t seconds. a. Find the maximum height that the weight rises above the equilibrium position of y 0. b. When does the weight first reach its maximum height, if t 0? c. What are the frequency and period? 9. Given cos s and tan s < 0, find sin s. 0. Given sin θ, cos θ < 0, find the remaining five trigonometric functions of θ.. Use identities to write sec x in terms of.

3 . Write + tan x + cot x Trig Exam Review F07 O Brien in terms of sine and cosine, and simplify so that no quotients appear in the final expression.. Verify the identity cos x + +. cos x cos x. Verify the identity tan A cos A sec A cos A. csc A. Verify the identity tan θ + cot θ sec θ csc θ.. Verify the identity csc x + cot x. cos x 7. Verify the identity ( sec x tan x) Verify the identity cos A + tan A tan A sin A. 9. Use the sum and difference identities to find the exact values of the cosine of 9. Do not use a calculator. 0. Use the sum & difference identities to write the following expressions as the sine, cosine, or tangent of a single angle. a. sin cos + cos sin b. tan x + tan x tan x tan x θ o. Find an angle that makes sec θ csc Given cos α, α in Quadrant IV, and sin β, β in Quadrant III, find 7 α β α β tan α β a. sin( ) b. cos( ) c. ( ). Write each expression in terms of a single trigonometric function: a. sin y cos y b. cos α sin α tan θ c. tan θ. Use the half-angle identities to find the exact values of the sine, cosine, and tangent of 7π.. Given. Given 0 cos θ with θ in Quadrant IV, find the sine, cosine, and tangent of θ. 8 α cot α with α in Quadrant III, find the sine, cosine, and tangent of. 7. Write cos 7x cos x as the sum or difference of two functions. 8. Find the exact value of cos 7. sin.. Do not use a calculator. θ θ 9. Write sin + sin as the product of two functions.

4 Trig Exam Review F07 O Brien 0. Evaluate 7π π cos cos. Do not use a calculator.. Find the exact degree value of θ sin. Do not use a calculator.. Use a calculator to find the degree measure of θ arccot (.).. Find the exact radian value of y cos. Do not use a calculator.. Give the exact value of sec (arcsin.). Do not use a calculator.. Find the exact value of the given expressions. Do not use a calculator except to get a final answer on b. a. cos arcsin b. tan cos sin. Find the exact solutions of csc x in the interval [0, 0 ). 7. Find the exact solutions of tan x + tan x in the interval [0, π). 8. Find the exact solutions of cos x 0 in the interval [0, 0 ). 9. Find the exact solutions of tan x + sec x in the interval [0, π). θ 0. Find the exact solutions of sin in the interval [0, π).. Find the exact solutions of cos x + cos x 0 in the interval [0, π).. Find the exact solutions of cos x in the interval [0, π). Answers. a. a, b, c π, d ; b. amp:, x-axis ref: yes; period: π, π π x-inc:, p.s.: right, v.t.: up c., π,,,, ; d. π. a. a, b, c, d ; b. amp:, x-axis ref: no; π π period: π, x-inc: π 7 c., π π,, p.s.: π left, v.t.: down 9, 7π, 0π 7, ; d.

5 Trig Exam Review F07 O Brien. a. a, b, c π, d ; b. x-axis ref: no; period: π, π x-inc: π π, p.s.: right, v.t.: up; c. LA: x, RA: d. lkp: (0, ), mkp:,, rkp:, ; e. π x ;. a. a, b, c π, d 0; b. x-axis ref: no; period: π, π π π π x-inc:, p.s.: left, v.t.: none; c. LA: x, RA: x 0; d. lkp: π π, 8, mkp:, 0 8, rkp:, 8 ; e.. Guide function: y sin x π a. a, b, c, d ; b. amp of sine:, x-axis ref: no; period: π, x-inc: c., - 8 π π π, p.s.: right, v.t.: down 8 8 π, 8, - 8 7π, - 8 9π 8, - ; d.. Guide function: y cos( x + π) + a. a, b, c π, d ; b. amp of cosine:, x-axis ref: yes; π π period: π, x-inc:, p.s.: π left, v.t.: up c.,, (0, ),, ; d. π b..0 units c. 8. a. inches b. after sec c. frequency cycles per sec; period sec 8 7. a. s() t cos t 9. sin s

6 Trig Exam Review F07 O Brien 0. cos θ ; tan θ ; cot θ ; sec θ ; csc θ. ± sec x. tan x. verification of identity - answers may vary - see instructor if you would like your verification checked. verification of identity - answers may vary - see instructor if you would like your verification checked. verification of identity - answers may vary - see instructor if you would like your verification checked. verification of identity - answers may vary - see instructor if you would like your verification checked 7. verification of identity - answers may vary - see instructor if you would like your verification checked 8. verification of identity - answers may vary - see instructor if you would like your verification checked 9. cos 9 0. a. sin 0 b. tan x. 0 o a. sin ( α β) b. cos ( α β) 97 c. tan ( α β) 0. a. sin y b. cos α c. tan 8θ. 7π + 7π 7π sin ; cos ; tan sin θ ; cos θ ; tan θ α α α sin ; cos ; tan 7. 7 [ cos 0x + cos x]. a. b. 8.. x 90, 0, 0 9. θ θ sin cos π π x,,.0, x,,,. 9. π x. o π π θ x,. π y. π π x, π,. π π π 7π. x,,,