Review for Exam IV MATH 1113 sections 51 & 52 Fall 2018
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1 Review for Exam IV MATH 111 sections 51 & 52 Fall 2018 Sections Covered: 6., 6., 6.5, 6.6, 7., 7.1, 7.2, 7., 7.5 Calculator Policy: Calculator use may be allowed on part of te exam. Wen instructions call for an exact solution, tat indicates tat a decimal approximation will not be accepted. Tis review is provided as a courtesy to give some idea of wat material is covered. Noting else is intended or implied. (1 Evaluate eac trigonometric expression exactly if it exists. (Ceck wit a calculator, but be able to do tis witout one. You can be sure I will ask you to do so on an exam. cos ( π 2 (b cot (2π (c csc ( 6 (d sin ( 11π 6 (e tan ( π (f cos ( (g sec ( 2 ( sec ( 2π (i tan ( (2 State te domain and range of eac of te six trigonometric functions. Use interval notation or set builder notation. ( Identify te amplitude and period of eac of eac function. ( x ( f(x = cos 2 (b g(x = sin πx + π 2 6 (c ( π F (x = sin 2x ( Consider eac trigonometric equation. Determine if te equation is an identity or if it is conditional (i.e. not an identity. If it is an identity, prove it. If it is not an identity, find at least one value of te variable for wic te equation is not satisfied. sin x 1 cos x = 1 + cos x sin x (b (cos θ + sin θ 2 = 1 (c sin 2 β tan 2 β = tan 2 β sin 2 β (d tan x + cot x csc x = sec x (e cos 2 t + cot 2 t = sin t sec t
2 (5 Given cos(u v = cos u cos v +sin u sin v and sin(u v = sin u cos v sin v cos u, obtain expressions for eac of te following. cos(u + v (b sin(u + v (c cos(2u (d sin(2u (6 Suppose sin α = 1 and cos β = 1 5. Futer suppose tat π 2 < α < π and π < β < π 2. Evaluate eac of te following exactly. cos(α β (b sin(2β (c sin(α + β (7 State te domain and te range of eac of f(x = sin 1 (x, g(x = cos 1 (x and H(x = tan 1 (x using interval notation. (8 Evaluate eac expression exactly if it exists. If it doesn t exist, state wy. sin ( sin (b sin 1 (sin 0.02 (c sin 1 [sin (π] (d cos 1 [ cos ( π (e cos (tan 1 (f csc [ cos ( ] 1 2 ] (9 Find an equivalent algebraic expression for eac of te following (algebraic meaning witout any trigonometric functions. sin ( sin 1 (2x (b cos ( sin 1 (2x
3 (c sec (tan 1 u (10 Use te sum of angles formula for te cosine tat you obtained in (5 to sow tat if f(x = cos x, ten f(x + f(x ( ( cos 1 sin = cos x sin x (11 Evaluate eac expression exactly. cos (ln(1 (b tan 1 (e 0 tan 0 (c e (d e cos 90 (e sin 1 (ln e (f cos 1 (ln 1 (12 Find all solutions of te given trigonometric equation on te interval [0, 2π. 2 sin x = 0 (b sin(2x + cos x = 0 (c tan 2 x = 1 (d 2 cos 2 x 1 = cos x (e sin x + 1 = 2 cos 2 x (1 Plot at least two full periods of eac of y = sin x, y = cos x, and y = tan x. (1 Matc te following functions wit te plots sown. Note tat not all of te functions will be used. f(x = 2 cos ( x + π (b f(x = sin(x (c f(x = 2 sin(2x + 1 (d f(x = cos x + 1 (e f(x = cos(x + 1 (f f(x = 1 2 sin(2x 2 (g f(x = 2 + cos ( πx π 2 ( f(x = cos ( x (i f(x = sin ( x π
4 Te following problem types would ave to appear on a part of te exam in wic calculator use is allowed. (15 Te our and on a certain clock is inces long. Determine te lengt of te arc traversed by te tip of te our and between 1 pm and 6 pm (on te same day, so in five ours.
5 (16 Te rear weel of a tractor as a 2 in radius. Find te angle (in radians troug wic a weel rotates in 11 sceonds if te tractor is traveling at a speed of 2 mp. (17 One gear weel turns anoter, te teet being on te rims. Te weels ave 0 cm and 50 cm radii, and te smaller weel rotates at 10 rotations per minute. Find te angular speed of te larger weel, in radians per second. (Te answers is actually better if you don t boter wit a calculator.
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