(c) cos Arctan ( 3) ( ) PRECALCULUS ADVANCED REVIEW FOR FINAL FIRST SEMESTER
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1 PRECALCULUS ADVANCED REVIEW FOR FINAL FIRST SEMESTER Work the following on notebook paper ecept for the graphs. Do not use our calculator unless the problem tells ou to use it. Give three decimal places on calculator problems. Show all work.. Find two angles, one positive and one negative, that are coterminal with the given angle. (a 5 (b 5 π 8. Convert 65 to radians. Give our answer in terms of π.. Convert π to degrees Graph = sin + π π/ π π/ π/ π π/ π 5π/ π 7π/ 5. Graph f ( = + if if < 6. If θ is in the third quadrant and cosθ =, find the values of the other five trig. functions of θ. 7. Give the eact value of the si trigonometric functions for each angle. (a 5 π (b 4 π 6 8. If f ( = + and g ( = 5, find: (a ( f + g( (b ( f g( (c g ( a (d f ( g ( 9. Find the value. (a Cos (b Arcsin ( (c cos Arctan ( 0. Find the value: (a sin Cos 5 (b tan Sin 7 8 (c 5 sec Arctan
2 . Solve in radians, 0 < π :. Solve in radians, 0 < π : sin sin = 0 cos + cos = 0. Use our calculator to find all values of θ, 0 θ < 60, for which cosθ = Simplif: csc cos cot. 5. Find the inverse of f ( = + 7. π 6. If sec = 5 and < < π, find the eact value of the other five trig. functions of. 7. Write the equation of a sine graph with amplitude, period π, and translation units up. 8. Find an angle coterminal with 00 that has a measure between 0 and Use a sum or difference identit to find the eact value of sin 75. π 0. Given cos A =, < A < π, draw a figure and find the value of sin A. 5. Find the value of cosθ if sinθ = andθ is in standard position with its terminal side in Quad. 4.. Solve in radians, 0 < π : cos sin = 0. Solve in radians, 0 < π : sin cos = 0 5 π 4 π 4. Given: sin A =, < A < π, and tan B =, π < B <, draw a figure and find: (a cos( A B (b cos A π 5. Graph = cos +. 4 π π/ π π/ π/ π π/ π 5π/ π 7π/ 6. Graph f ( = + if if <
3 7. Match the graph to the correct equation. A. = cos + B. = cos + C. = sin D. = sin + 8. Solve in radians, 0 < π : cos( = 9. Find cos θ, given sinθ = 5 and tanθ < Evaluate: Cos. Evaluate: sec ( Arctan. Epress 0 in radians.. Use our calculator to epress in decimal degrees. 4. Use our calculator to epress in degrees, minutes, and seconds. 5. Find the domain of the following functions: (a f ( 4 6. Find the domain and range of =. π 7. Graph = tan + 4 = (b = 4 9 π π/ π π/ π/ π π/ π 5π/ π 7π/ 8. Determine the values of 0 < π, for which cscθ =. 9. Which of the following is equivalent to cos( 50? A. cos 50 B. cos 0 C. cos( Graph ( if 0 f = if 0 < < if 4. Evaluate: csc 90 + cot 0 + sin 80 + cos 70
4 4. If g ( = + f ( = + f ( g ( and, find. 4. Evaluate using our calculator: csc Given tanθ =.67, use our calculator to find all values of θ in radians, 0 θ < π. 45. Solve in radians, 0 < π : cos cos = 0 7π 46. Use a sum or difference identit to find the eact value of cos. 47. Given: cos A =, sin B =, neither A nor B is in quadrant III. Find: (a cos( A + B (b sin A Simplif: tan + sin + cos 49. Graph = cot. π π/ π π/ π/ π π/ π 5π/ π 7π/ f below, graph the following: 50. Given the graph of ( (a g ( f ( = + Graph of f (b h( f ( = + What is the domain of h(? What is the range of h(?
5 5. As ou ride the Ferris wheel, our distance from the ground varies sinusoidall with time. Let t be the number of seconds that have elapsed since the Ferris wheel started. You find that it takes ou seconds to reach the top, 4 ft. above the ground, and that the wheel makes a revolution once ever 8 seconds. The diameter of the wheel is 40 ft. (a Sketch a graph of a complete ccle. (b Write an equation for this sinusoid. (c Use our calculator to find our height above the ground when t = 4 seconds. (d Use our calculator to find the value of t the second time ou are 8 ft above the ground. 5. Graph = sec + π π/ π π/ π/ π π/ π 5π/ π 7π/ 5. If sec θ > 0 and cotθ < 0, in which quadrant would ou find θ? Determine the value of sin Cos Solve in radians, 0 < π : sin + sin = Given f ( = + g ( = g ( f (, 5, find. 57. Write the equation of a cosine curve with a maimum value of 5, a minimum value of, π and a period of. 58. State the tpe of smmetr of f ( = Solve in radians, 0 < π : sin cos = Find the length of an arc in a circle of radius 9 in. that is intercepted b a central angle of 0. (Leave our answer in terms if π. 6. Find the area of a sector of a circle of radius 8 cm that is intercepted b a central angle of 5 π. 4 (Leave our answer in terms if π.
6 π 6. Graph = cos + 4 π π/ π π/ π/ π π/ π 5π/ π 7π/ 6. Graph ( if < f = if < if PRECALCULUS ADVANCED FORMULAS YOU HAVE TO KNOW FOR THE FIRST SEMESTER EXAM Pthagorean Identities Cofunction Identities π cos θ + sin θ = cos = sin π + tan θ = sec θ sin = cos + cot θ = csc θ Sum and Difference Identities ( ( sin A ± B = sin Acos B ± cos Asin B cos A ± B = cos Acos B m sin Asin B tan tan A ± tan B ± = m tan Atan B ( A B Double-Angle Identities sin θ = sinθ cosθ cos θ sin θ cos θ = sin θ cos θ tanθ tan θ = tan θ
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