MAC 1114 REVIEW FOR EXAM #2 Chapters 3 & 4

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1 MAC 111 REVIEW FOR EXAM # Chapters & This review is intended to aid you in studying for the exam. This should not be the only thing that you do to prepare. Be sure to also look over your notes, textbook, and homework. Section.1 In questions 1 name the reference angle for each angle below In questions 5 use your calculator to find θ to the nearest tenth of a degree if 0 < θ <.. cos θ = with θ in QIV 5. tan θ = with θ in QIII. Find θ, if 0 < θ < and cot θ = with θ in QIII. Section. In questions 7 9 label the reference angle in both degrees and radians In questions 10 1 write each of the following in degrees In questions 1 15 convert to radians

2 In questions 1 18 give the exact value of the following: 1. sin 17. cos sec In questions 19 0 evaluate each of the following where x is and y is. 19. cos( x + y) 0. cos x + cos y 1. θ is a central angle that cuts off an arc of length s. Find the radius of the circle if θ = and s = / cm. Section. In questions - use the unit circle to find the six trigonometric functions of each angle. Use exact values for your answers In questions 5 use the unit circle to find all values of θ between 0 and to satisfy each equation. Write your angles in exact radian measure.. cosθ = 5. cot θ = 1

3 In questions 8 use the unit circle and the even/odd properties of the trigonometric functions to find each of the following. Use exact values for your answers.. tan 7. csc 8. cos 9. What will be the value of the expression cos +? 0. If angle θ is in standard position and intersects the unit circle at the point 1,, determine sin θ, cos θ and tan θ. Use exact values. 1. Prove the identity by transforming the left side into the right side. sin( θ) tan( θ)cos( θ) = sin θ Section.. The minute hand of a clock is. cm long. How far does the tip of the minute hand travel in 0 minutes? For the answer, use exact form and then approximate to one tenth of a cm.. Find the area of the sector formed by a central angle of 5 in a circle of radius 8 inches. State the area in exact form.

4 Using the Unit Circle. Use the unit circle to find all values of x between 0 and for which the equation is true. Write your angles in exact radian measure. tan x = 1 5. Find all values of x for which (a) cos x = 0 (c) tan x = 0 (b) sin x = 0 (d) cot x = 0 Sections.. In questions 0 graph one complete cycle. Find exact values for the beginning, middle, end, quarter and three-quarter points of the cycle. 1. y = 1 + sin x 7. y = cos x 8. y = cscx 9. y = sec x

5 1 0. y = sin x + 1. y = cos x. y = tan x. y = cot x Section.5 In questions 5 one complete cycle of the graph of a trig function is given below. Find an equation to match the graph.. 5.

6 Section.7 In questions 51 evaluate each expression without a calculator, and write your answers in radians.. cos 1 (0) 1 7. tan 1 8. sin 1 9. Use a calculator to evaluate sin 1 ( 0.170) to the nearest tenth of a degree Evaluate tan cos 5 without using a calculator Evaluate sin cos without using a calculator. 5

7 MAC 111 Answer Key Review o o,5 8. o,0 9. o, r = /8 cm. 11 sin = 11 csc = 1 11,cos = 11,sec = 1 11,tan = 1, 11,cot = 1. sin = 1,cos = 0,tan undefined, csc = 1,sec undefined,cot = , 5., cos = sin θ =,cosθ =,tanθ = sin( θ ) 1. sin θ cos( θ ) = sinθ cos( θ ) sin θ + sinθ = sinθ sinθ = sinθ.. 8. cm. 8 square inches x =,,, 5. (a) k where k is any odd integer 7 ±,,,,... (b) k where k is any integer ± { 0,,,,,... } (c) k where k is any integer (d) { 0,,,,,... } ± k where k is any odd integer 7 ±,,,,...

8 . up one, amplitude =, new period is beginning: (0, 1) one-quarter: (, ) relative max one-half: (,1) three-quarter: (, ) relative min end: (, 1) 7. amplitude is, new period is beginning: (0, ) relative max one-quarter: (1/, 0) x-intercept one-half: (1, )relative min three-quarter: (/, 0) x-intercept end: (, ) relative max 8. amplitude is 1, new period is beginning: asymptote at x = 0 one-quarter: (/, 1) relative min one-half: asymptote at x = / three-quarter: (/, 1) relative min end: asymptote at x = /. asymptotes at ±, x-intercept at (0, 0). asymptotes at x =, x =, x-intercept at (/, 0). y = sin( x) 5. 1 y = 9 cos x amplitude is 1, new period is / beginning: (0, 1) relative min one-quarter: asymptote at x = / one-half: (/, 1) relative max three-quarter: asymptote at x = end: (/, 1) relative min 0. amplitude is 1, period is, phase shift is left / beginning: ( /, 0) x-intercept one-quarter: (/, 1) relative max one-half: (/,0) x-intercept three-quarter: (/, 1) relative min end: (7/, 0) x-intercept 1. amplitude is 1/, new period is /, phase shift is right / beginning: (/, 1/) relative max one-quarter: (/, 0) x-intercept one-half: (/, 1/) relative min three-quarter: (/, 0) x-intercept end: (/, 1/) relative max