NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part 2 Trigonometry, 10th Edition; Lial, Hornsby, Schneider Spring 2013
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1 NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part Trigonometry 0th Edition; Lial Hornsby Schneider Spring 0 Departmental Final Exam Review for Trigonometry Part : Chapters and Departmental Objectives: [indicates corresponding MML questions]. Graphing the six trigonometric functions by hand. [Sections:....]. Analyzing and writing equations of simple harmonic motion. [Section:.]. Verifying and applying trigonometric identities and solving trigonometric equations. [Sections: ]. Defining using and applying inverse trigonometric functions. [Sections:...] Chapter : Graphs of Circular Functions. Given y sin x - π a. Find: amp: x-axis reflection: period: b. Find: key points: c. Manually graph two periods of the given function. [..]. π Given y cos x a. Find: amp: x-axis reflection: period: b. Find: key points: c. Manually graph two periods of the given function. [..]. π Given y tan x a. Find: x-axis reflection: period: b. Find: left asymptote: x = right asymptote: x = c. Find: left key point: middle key point: right key point: d. Manually graph two periods of the given function. [..9]
2 NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part Trigonometry 0th Edition; Lial Hornsby Schneider Spring 0. Given y cot x π a. Find: x-axis reflection: period: b. Find: left asymptote: x = right asymptote: x = c. Find: left key point: middle key point: right key point: d. Manually graph two periods of the given function. [..]. π Given y csc x - a. Find: amp of sine: x-axis reflection: period: b. Find: key points of sine c. Manually graph two periods of the given function. [..7]. Given y sec x + π a. Find: amp of cosine: x-axis reflection: period: b. Find: key points of cosine c. Manually graph two periods of the given function. [..] 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. [..9] 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.. The height attained by a weight attached to a spring set in motion is s(t) = cos πt inches after t seconds. [..7] 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?
3 NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part Trigonometry 0th Edition; Lial Hornsby Schneider Spring 0 Chapter : Trigonometric Identities 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. [..]. Write tan cot x x in terms of sine and cosine and simplify so that no quotients appear in the final expression. [..79]. Verify the identity tan A cos A sec A cos A. [..] csc A. Verify the identity sec x tan x sin x. [..7] sin x. Verify the identity cos A tan A tan A sin A. [..]. Use the sum and difference identities to find the exact values of the cosine of 9. Do not use a calculator. [..9]. Given cos α α in Quadrant IV and sin β β in Quadrant III find [....7] 7 α β α β tan α β a. sin b. cos c. 7. Use identities to find the exact value of [..9]. Use the half-angle identities to find the exact values of the sine cosine and tangent of 9. [.. ] 9. Given 0. Given 0 cos θ with θ in Quadrant IV find the sine cosine and tangent of θ. [..] α cot α with α in Quadrant III find the sine cosine and tangent of. [..9 ] Chapter : Inverse Circular Functions and Trigonometric Equations. 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. [..]
4 NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part Trigonometry 0th Edition; Lial Hornsby Schneider Spring 0. 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. c. tan cos sin [.. 7 9]. Find the exact solutions of sin x = csc x in the interval [0 0 ). [..]. Find the exact solutions of tan x tan x in the interval [0 π). [..7] 7. Find the exact solutions of tan x + = sec x in the interval [0 π). [..] θ. Find the exact solutions of sin in the interval [0 π). [..] 9. Find the exact solutions of cos x cos x 0 in the interval [0 π). [..]
5 NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part Trigonometry 0th Edition; Lial Hornsby Schneider Spring 0 Answers Chapter : Graphs of Circular Functions. a. amp: x-axis ref: yes; period: π π p.s.: right v.t.: up π π b. π π π ; c.. a. amp: x-axis ref: no; period: π p.s.: π 7 b. π π left v.t.: down π π 9 7π 0π 7 ; c.. a. x-axis ref: no; period: π p.s.: π π π right v.t.: up; b. LA: x RA: x ; π π c. lkp: (0 ) mkp: rkp: ; d. π. x-axis ref: no; period: π π p.s.: left v.t.: none; b. LA: π x RA: x = 0; c. lkp: π π π mkp: 0 rkp: ; d.
6 NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part Trigonometry 0th Edition; Lial Hornsby Schneider Spring 0 π. Guide function: y sinx a. amp of sine: x-axis ref: no; period: π p.s.: π right v.t.: down π b. - π π - 7π - 9π - ; c.. Guide function: y cos x π a. amp of cosine: x-axis ref: yes; π period: π p.s.: π = left v.t.: up π π π π b. (0 ) ; c. 7. a. st cos t π b..0 units c.. a. inches b. after sec c. frequency = cycles per sec; period = sec Chapter : Trigonometric Identities sin s cos θ ; tan θ ; cot θ ; sec θ ; csc θ. 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. cos 9 97 sin α β 0. a. b. cosα β c. tanα β sin9 ; cos sin θ ; cos θ ; α sin ; α cos ; tan θ α tan ; tan9 70 9
7 NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part Trigonometry 0th Edition; Lial Hornsby Schneider Spring 0 Chapter : Inverse Circular Functions and Trigonometric Equations... θ π y. a. b. c. 7. x = π π. x = π x. π π x = 9. π π x = π 7
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