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Name ____________________ Precalculus, Period _________ Date:____________ Teacher:_________ REVIEW for the FINAL EXAMS Precalculus A, First Semester Answer/Solve the following questions/problems. Show work completely & neatly to receive full credit. Part 1: Beginning Trig 1. Give 3 angles that are coterminal with 50o. 2. Convert to 195o to radian measure. Leave answer in terms of π. 3. Covert 7π/3 to degrees. 4. If sin x = 1/3 in quadrant II, find the other 5 trig values 5. If the terminal side of angle contains the point (-4, 4), find the 6 trig values. Trig Functions 6.a) Find sec if cos = 2 3 7 Pre-AP) . Evaluate sec , if sin 6.b) 7 and tan >0 10 Find tan if sin = 6 7 8. Find the A, B, C, & D, then write an equation for each graph. a. b. 9. For each equation, give the Principal Axis (vertical shift), Amplitude, Period, Phase Shift, Max & Min, and Range. 5 2 (x 3) 3 a. y = cos 2 3 (Vertical shift, D) =____, Amp. (A) = ____, Per.=____, Ph.Shft. (C) =____, Range: _______ Per.=____, Ph.Shft. (C) =____, Range: _______ Per.=____, Ph.Shft. (C) =____, Range: _______ 5 b f ( x) sin x 6 . 4 2 (Vertical shift, D) =____, Amp. (A) = ____, 3 x 3 c. f ( x) 3 50 cos 4 (Vertical shift, D) =____, Amp. (A) = ____, d. f ( x) 3 50sin 4 x 3 (Vertical shift, D) =____, Amp. (A) = ____, e. Per.=____, Ph.Shft. (C) =____, Range: _______ Per.=____, Ph.Shft. (C) =____, Range: _______ f ( x) sin 3x (Vertical shift, D) =____, Amp. (A) = ____, 10) . Which of the following choices is the equation for the given graph: A) y= 5sin(x) B) y= –5cos(x) C) y= –5sin(x) D) y= 5 cos (x) 11). The diagram below shows the curve y = p + k cos (ax) Find the value of p and k. Linear and Angular Velocity (Pre-AP) 12. The diameter of a merry-go-round is 10 ft. If it turns at 6 rpm, what is the linear velocity a) in feet per minute b) in mph on its outer edge? 13. The diameter of a motorbike’s wheels is 30 inches. Find the angular velocity in (revolutions per minute) rpm, if the motorbike is traveling at 40 mph. 14. Find the radius of the circle from which a sector is cut off. The area of the sector is 36 in2, and its central angle is 10 9 15) Find a, b, & c. 16) RIGHT Triangle Trigonometry 17) 18) Find the angle of elevation of a ramp that is 50 ft long and which rises to a maximum height of 20 ft. 19) Pre-AP Graphing Sinusoids Pre-AP Graph one cycle of each. 20. Y = 5cos(4X) 21. Y = 6 + 4sin(2πX) ----------------------------------------------------------------------------------------------------------------------------- -- 22. Graph y= -2sin(2(x-/4))+3. (Hint: Maybe you need to visualize this first? y = -2sin(2(x))+3 Simplifying Trig Expressions (answers must be in exact values) cosq ____23) Identify the value of that makes the expression undefined. 1- sin 2 q a. 90o b. 180o c. 270o d. 360o 24) If cos θ = 0.891, what is sin 2 θ? Trig Identities and Equations 17. Simplify: (sin x)(cot x)(sec x). 19. Simplify: csc x - (cos x)(cot x) 18. (sec y tan y )(sec y tan y ) sec y 20. Simplify: sec x sin x – sin x cos x 21.Simplify: 1 – cos2x 1 – sin2x 22. Simplify: sin(2x) sin x 23. 1 1 1 sin x 1 sin x 24. tan x(1 sin 2 x) 25. sin(2 x) cos 2 x sin 2 x 28. 1 cos x Solve the folloring trig equations in the domain [0, 2 27. 2cos x – √3 = 0, 32 2 tan x cos x tan x 0 28. 3tan2 x = 1, 29. 1 – sin2θ = 2, 33. sin(2x) = sin x 30. cos 2x – cos x = 0 34. 2sin 2 x 3sin x 2 31. 4cos2 x 4cos x 1 0 38. If tan x = 1.3, then what does tan x + cot x equal to? Law of Cosines, Law of Sines, SAS Area 39. In a triangle with side lengths 10, 12, and 15, find the measure of the largest angle. 40. In triangle DEF, D = 60o, E = 15o, d = 17 cm. Find the length of side e. 41. In triangle PQR, p = 5, q = 12, and R = 40o. Find the length of side R. 42. In triangle ABC, A= 30o, b = 10, c = 15. Find the area. 43. Find the area of a triangle with side lengths 5, 7, and 9. 44. A farmer is estimating the surface area of his barn to find how much paint he needs to buy. Shown below is a triangular part of the barn which will be painted red. a. Find the area of the triangle. 28° 28° 6018 ft m b). One quart of paint that costs $14.96 can cover about 85 ft2. How much will it cost to paint the triangle? 45. VECTORS 46.. Given the points P(8, -2) and Q(-3, -5), find PQ and |PQ|. 47. Given vectors a = ‹ 2, 4 › and b = ‹ -1, 7 ›, find 3a – 2b. 48. Given vector a = ‹ -2, -8 › and vector b = ‹ 12, -4 › , find the magnitude of |a+b| 49. Find the unit vector for 7i + 2j. 50. Given a = ‹ -2, 5 › and b = ‹ -1, -3 ›, find the dot product a∙b. 51. Find the angle between vectors p = 4i – 3j and q = 2i + 5 Find the components of the following vectors: Find the area of the shaded portion of the circle. How many triangles can be possibly formed given the following conditions: 1) A = 36o; a = 2; b = 7 2) B = 30o; b = 3; c = 6 2) What is the standard measure of the angle determined by the point (–2, 2). 3) Find the radius of a 110o arc that is 10 inches long.