Trigonometry Winter E.C. Packet

Transcription

1 Name: Class: Date: Trigonometry Winter E.C. Packet 1. *MUST SHOW WORK/COMPUTATION for all problems (these problems are designed to not to use a calculator except for Law of Sines/Cosines) *All work must be clear, neat, and organized according to the order the problems are assigned - if I have trouble locating or reading your work, no credit will be given. *For every 10 problems = 1 assignment point Determine which of the following points will lie on the line through the points (-, ) and (0, 4): a. (0,-) d. (66, -) b. (44, 8) e. None of these c. (11, -6). Factor completely n n. Factor completely x 7 8x 5 4x 4. Factor completely 5x x Factor completely x 4 + x 4x 1x 6. Factor completely 10x 5 160x 7. Factor completely 40x 4 + 5xy 9 8. Find the real-number solutions x 5 x 4 5x + 5x + 4x 4 = 0 9. Find the real-number solutions x 4 5x + 8x 4x = Find the real-number solutions x 5 + 5x = 6x 11. ( x 1) 4( x 1) 1 + = 0 Factor and solve. 1. x x = 1 solve 4 1. x + = solve 14. List the possible rational zeros of the function using the rational zeros theorem. h(x) = x 4 5x x + 7x Find all real zeros of the function. f( x) = x 4 + x x 11x 6 1

2 Name: 16. Find all zeros of the polynomial function. f( x) = 6x 4 5x 1x + 5x Write a polynomial function f of least degree that has rational coefficients and the given zeros. 1, 1, Write a polynomial function f of least degree that has rational coefficients and the given zeros. ± i, Let f( x) = 1 x and g( x) = 1 x. Find f û g( x). 0. Let g( x) = x and h( x) = x + 1. Find hû g( ) 1. x 8 = 5 Solve. x + 5 = x. Find the height of the building when A = 5. *Calculator needed 4. In the diagram, VW Ä ZX. If YX = 5, what is ZX? *Calculator needed 5. Find the missing side lengths for x and y.

3 Name: 6. Solve ABC using the diagram and the given measurements. (Note: The triangle is not drawn to scale.) B = 4, a = 7 7. Graph and label all asymptotes: f( x) = x x 4 8. Graph y x + 9. Graph y > x 1 0. Use the graph to determine the domain and range of the relation, and state whether the relation is a function. 1. Find the zero of the function f( x) = 5x.. Determine the standard form of the equation of the line that passes through Ê 7, 8 ˆ and Ê 0, 8 ˆ.. Find an equation of the line perpendicular to the graph of 14x 7y = 8 that passing through the point at Ê, 5ˆ.

4 Name: Ï 4 if x < 5 4. Graph f(x) = Ô Ì x if 5 x 8 4 x if x > 8 ÓÔ 5. Solve the system of equations. 5x + 9y + 9z = 5 4x + 9y + 6z = 10 x + y + 5z = 9 6. Solve x + 8 > Given: Then state whether f 1 ( x) is a function. 8. Graph and label all asymptotes: y = x 9 x Decompose x, into partial fractions. ( x 4) ( x ) 40. Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (, 0) lies on its terminal side. 41. If c = and B = 69, find a. Round to the nearest tenth. Ê Ê 4. Evaluate the expression. Assume that all the angles are in Quadrant I. cos arctan ˆˆ 7 4. Solve the equation if 0 x 60. A) cos x = 1 B) sinx = 4

5 Name: 44. Find the area of the triangle with A = 4, b = 8 feet, and c = 5 feet. Round to the nearest tenth. 45. Given a triangle with b =, c = 7, and A = 4, what is the length of a? Round to the nearest tenth. Ê 46. graph the function. y = 4cos θ + ˆ π + Ê 47. Graph y = tan 1 ˆ 4 θ + π Graph x y 1 x + 4y Solve x + 5y z = 18 x y + 5z = x y + 8z = Rationalize: 6 + i i 51. Find the vertex form of the equation then graph: y = x 1x Write an equation for the parabola with the given vertex and passes through the given point. vertex (1,) point (, 15) 5. Simplify 54. Simplify x + x + 5x x x + x 6 = x + x + 4 x + x + 1 = 55. Simplify x 10 x + 9 x 5 x + 4 = 56. Solve x + x + x + 5 x + = 1 x 5

6 Name: 57. a) tan π 4 = b) cos 4π = c) cot( π) = d) sin( π 4 ) = e) tan 1π Solve the triangle (all sides and angles): A = 45 Ο, a = 15cm, b = 18cm 59. Solve the triangle: C = 5 Ο, a = 5cm, b = 8cm Ê 60. A)cos 1 ˆ = B)Sin 1 = C)Arc tan = D)Arc cos ( 1 ) = 61. Graph y = tan( x π) Ê 6. Graph y = tan x π ˆ 6. Graph y = sec x Graph y = cos Ê x + 0 Ο ˆ sec θ =? if tanθ = 4 and 180 Ο < θ < 70 Ο 66. Graph y = ( x + ) 67. y 8x = 9 Find the points of intersection, if any, of the graphs in the system. y = 4x 68. Graph y = x + 8x Solve the triangle (the angles, in this case) if a = 18cm, b = 10cm, c = 9cm 70. Graph y = csc θ 6

7 Trigonometry Winter E.C. Packet Answer Section 1. B. n Ê ( n + 6) n ˆ 6n + 6. x Ê x ˆ + Ê x 7 ˆ Ê 4. 5 x ˆ + ( x 1) ( x + 1) 5. x( x ) ( x + ) ( x + ) Ê 6. 10x x ˆ + 4 ( x + ) ( x ) 7. 5x Ê x + y ˆ Ê 4x xy + y 6 ˆ 8. x = 1; ; 1; ; ; ; ; ±1, ± x = and ± 1 ± 1,± 15., 1, 16. 1, 1,, 17. f( x) = x + x 6 x f( x) = x 8x + 9x x + x about 105 ft. 4. About x = 4, y = 4 6. A = 47 o, b = 6.5, c =

8 7. x =, x = Domain: all real numbers; Range: {y 1 y 1}; Yes, for any value of x there is only one value of y.

9 x 7y = 56. y = 1 x x = 116, y = 8, z = 7 Ï 6. x x > 1 Ô Ì or x < 17 Ô ÓÔ Ô increasing for x < 9 and x > 1; decreasing for 9 < x < 5 and 5 < x < 1 4 ( x 4) + ( x ) 40. sin α = 0, cos α = 1, tan α = 0, csc α = undefined, sec α = 1, cot α = undefined 41. a = 8.

10 A) 10, 40 B) 5, units ; π; 1 π ; ,, i 6 4

11 y = (x 1) x (x + )(x + 1) 55. x + 14x + 40 x + 14x , ; 1 ; undef; ; 58. B 58degrees,C 77degrees,c 0.7cm or B 1 deg rees,c 1deg rees,c 4.8cm 59. A 7 Ο B 108 Ο c A)150 Ο B)60 Ο C)60 Ο D)10 Ο 61. 5

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13 (0, ), (, 5) (, 5) 68. Answer: 69. A 14 Ο B 0 Ο C 18 Ο 70. 7