Trigonometry Final Exam Questions
Course Introduction
Trigonometry is a branch of mathematics that explores the relationships between the sides and angles of triangles, with a primary focus on right-angled triangles. This course covers fundamental concepts such as trigonometric functions, identities, and equations, as well as their applications in solving real-world problems. Students will learn to use the unit circle, graph trigonometric functions, and work with inverse trigonometric operations. Emphasis is placed on analytical problem-solving, modeling periodic phenomena, and connecting trigonometry to other areas of mathematics and sciences.
Recommended Textbook
Precalculus 2nd Edition by John W. Coburn
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12 Chapters
1334 Verified Questions
1334 Flashcards
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Chapter 1: Equations and Inequalities
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107 Verified Questions
107 Flashcards
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Sample Questions
Q1) Write the complex number in the standard form a + bi and clearly identify the values of a and b.
-2
Answer: -2 + 0i; a = -2, b = 0
Q2) Simplify using powers of i. i<sup>64</sup>
A) 1
B) -1
C) i
D) -i
Answer: A
Q3) The length of a garden is 5 ft less than twice its width. The area of the garden is 88 ft<sup>2</sup>. Find the length and width of the garden.
Answer: 11 ft, 8 ft
Q4) Solve using the zero product property. Be sure each equation is in standard form and factor out any common factors before attempting to solve. Check all answers in the original equation. -5x<sup>3</sup> = -13x<sup>2</sup> - 6x
Answer: 11ea7f29_4fa9_404c_9ecd_698845ed82c7_TB3307_11
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Page 3
Chapter 2: Relations, Functions and Graphs
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196 Verified Questions
196 Flashcards
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Sample Questions
Q1) Determine the value of f(-6) if f(x) = -x<sup>2</sup> - 4x.
A) 30
B) -12
C) 36
D) -40
Answer: B
Q2) Find h(x) = f(x) + g(x).
A) h(x) = 8x<sup>2</sup> + x + 5
B) h(x) = 8x<sup>2</sup> - 2x + 5
C) h(x) = 8x<sup>2</sup> - 2x + 8
D) h(x) = 3x<sup>2</sup> + 3x + 8
Answer: A
Q3) Find h(x) = (g f)(x).
Answer: h(x) = x<sup>2</sup> - 3x - 3
Q4) State the domain of h(x) = (f ? g)(x).
A) x \(\in\) (1, ?)
B) x \(\in\) [1, ?)
C) x \(\in\) (-2, ?)
D) x \(\in\) [-2, ?)
Answer: B
Page 4
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Chapter 3: Polynomial and Rational Functions
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Sample Questions
Q1) Use the intermediate value theorem to verify that the polynomial f(x) = -2x<sup>3</sup> - 4x<sup>2</sup> + 3x - 4 has at least one zero "c<sub>i</sub>" in the interval [-3, -1]. Do not find the zeroes.
A) Yes
B) No
Answer: A
Q2) Find the intercepts. Round to the nearest tenth if necessary. f(x) = 3x<sup>2</sup> + 8x - 6
Answer: (-3.3, 0), (0.6, 0), (0, -6)
Q3) Use the rational roots theorem to write the function in factored form and find all zeroes. Note a = 1. p(x) = x<sup>3</sup> + 4x<sup>2</sup> - 9x - 36
Answer: (x - 3)(x + 4)(x + 3); x = 3, -4, -3
Q4) Factor completely. Then state the multiplicity of the roots and the degree of P. P(x) = x<sup>3</sup> - 2x<sup>2</sup> - 15x + 36.
Answer: P(x) = (x + 4)(x - 3)<sup>2</sup>; x = -4, root of multiplicity 1; x = 3, root of multiplicity 2; degree 3
Q5) Write the variation equation.
Answer: y = 11ea7f29_4fda_d732_9ecd_17303374ffda_TB3307_11
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Chapter 4: Exponential and Logarithmic Functions
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Sample Questions
Q1) Solve using any appropriate method. Clearly identify any extraneous roots. If there are no solutions, so state. log(x + 20) - log x = log(x + 2)
A) x = -5, 4
B) x = 4, -5 is extraneous
C) x = 5, 4 is extraneous
D) No solution
Q2) Determine the value of x by writing the equation in exponential form. log<sub> 2 </sub>x = 5
Q3) t = 7
A) 99.473
B) 103.724
C) 107.618
D) 111.831
Q4) Determine if the function is one-to-one by noting the functions family to which it belongs and mentally picturing the shape of its graph. f(x) = 8x<sup>2</sup> + 5
A) one-to-one
B) not one-to-one
Q5) t = 8.5
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Chapter 5: Introduction to Trigonometric Functions
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Sample Questions
Q1) State the quadrant of the terminal side of \(\theta\) using the information given. csc\(\theta\) < 0, Tan\(\theta\) > 0
A) QI
B) QII
C) QIII
D) QIV
Q2) Draw the graph of y = 3 sec t by applying observations made in this chapter about the related cosine graph.
Q3) State the quadrant of the terminal side and the sign of the function in that quadrant. Then evaluate the expression using a calculator. Round to four decimal places. csc 669°
Q4) Use a calculator to find the value of tan 34°, rounded to four decimal places.
Q5) Find the exact value of sin\(\theta\), cos\(\theta\), and tan\(\theta\) using reference angles. \(\theta\)= 225°
Q6) Find the value of the six trigonometric functions given P(4, -12) is on the terminal side of angle \(\theta\), with \(\theta\)in standard position.
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Chapter 6: Trigonometric Identities, Inverses, and Equations
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97 Flashcards
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Sample Questions
Q1) Rewrite as a single expression. cos(6\(\theta\) )cos(2\(\theta\) ) + sin(6\(\theta\) )sin(2\(\theta\) )
A) cos(8\(\theta\) )
B) cos(4\(\theta\) )
C) sin(8\(\theta\) )
D) sin(4\(\theta\) )
Q2) Verify the equation is an identity using special products and fundamental identities. (1 + cos x)[1 - cos(-x)] = sin<sup>2</sup> x
Q3) State the number of roots in [0, 2\(\pi\)].
A) 4
B) 3
C) 2
D) 1
Q4) Rewrite as a single expression. cos(10\(\theta\))cos(6\(\theta\) )sin(10\(\theta\) )sin(6\(\theta\) )
A) cos(16\(\theta\))
B) cos(4\(\theta\) )
C) sin(16\(\theta\) )
D) sin(4\(\theta\) )
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Chapter 7: Applications of Trigonometry
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86 Flashcards
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Sample Questions
Q1) Solve using the nth roots theorem. Approximate answers to four decimal places. x<sup>5</sup> - 1024 = 0
Q2) Solve the triangle using the law of sines. If the law of sines cannot be used, state why. Round sides to the nearest tenth.
\(\angle\)B = 21° side a = 18 yd
\(\angle\)C = 84°
Q3) Find the acute angle \(\theta\) formed by the vector and the nearest x-axis. Round to the nearest tenth of a degree.
Q4) Compute u + v.
A) i + j
B) 9i - 7j
C) 9i - 6j
D) 8i - 7j
Q5) Use De Moivre's Theorem to compute (4 + 4i)<sup>4</sup>.
A) 1024
B) -1024
C) 1024i
D) -1024i
Q6) Graph the vector.
Page 9
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Chapter 8: Systems of Equations and Inequalities
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Sample Questions
Q1) Whitney invested $8,000, part at 14% and part at 8%. If the total interest at the end of the year is $940, how much did she invest at each rate?
Q2) Solve the linear inequality by shading the appropriate half plane. 3x + y \(\le\) 5
Q3) Solve the linear inequality by shading the appropriate half plane. -3x + y \(\ge\) 0
Q4) Determine which of the ordered pairs given produces the maximum value of P(x, y). P(x, y) = 20x + 50y; (0, 0), (5, 2), (4, 0), (0, 6)
A) (0, 0)
B) (5, 2)
C) (4, 0)
D) (0, 6)
Q5) Find any four ordered triples that satisfy the equation. x - y + z = -3
Q6) Determine whether the ordered pair (0, 0) is a solution. 10x - 3y > 5
A) Yes
B) No
Q7) Solve the linear inequality by shading the appropriate half plane. x - y \(\le\) 2
Page 10
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Chapter 9: Analytical Geometry
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122 Verified Questions
122 Flashcards
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Sample Questions
Q1) Identify the equation as that of an ellipse or a circle. 5(x - 5)<sup>2</sup> + 5(y + 7)<sup>2</sup> = 80.
A) ellipse
B) circle
Q2) Convert from rectangular coordinates to polar coordinates. A diagram may help. (8, -8)
Q3) Show the figure drawn by connecting points A(-3, 1), B(4, -5), C(5, -1), and D(-2, 5) is a parallelogram (opposite sides parallel and equal in length).
Q4) State the domain and range.
A) x \(\in\) (-\(\infty\), 1]; y \(\in\)(-\(\infty\), \(\infty\))
B) x \(\in\)(-\(\infty\), \(\infty\)); y \(\in\) (-\(\infty\), 3]
C) x \(\in\) [3,\(\infty\)); y \(\in\) (-\(\infty\), \(\infty\))
D) x \(\in\)(-\(\infty\), \(\infty\)); y \(\in\) (-\(\infty\), \(\infty\))
Q5) Find the vertex.
Q6) Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. 25y<sup>2</sup> - 4x<sup>2</sup> = 100
Q7) Find the vertex.
Q8) Find the polar equation modeling the orbit of Mercury.
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Chapter 10: Additional Topics in Algebra
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121 Verified Questions
121 Flashcards
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Sample Questions
Q1) Jim deposits $15,000 in an account on January 1. Starting on January 2, he withdraws $100 each morning. Find the amount in his account on the evening of January 27. (Hint: For a<sub>1</sub> = 15,000, the amount remaining 26 days later will be what term of the sequence?)
A) $12,700
B) $12,600
C) $12500
D) $12,400
Q2) Find the sum S<sub>11</sub> for a geometric sequence with a<sub>1</sub> = 9 and r = -2.
Q3) Find the first four terms and write them as a list.
A) 1, -2, 3, -4
B) -1, 2, -3, 4
C) 2, -3, 4, -5
D) -2, 3, -4, 5
Q4) Find the sum of the first 20 multiples of 6.
Q5) Alex has 6 shirts, 6 pairs of pants, and 5 pairs of shoes. How many outfits can he wear?
Q6) Predict the next term for the sequence.
Q7) What is the probability the student answered "No" and is a boy?
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Chapter 12: Review of Basic Concepts and Skills
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112 Verified Questions
112 Flashcards
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Sample Questions
Q1) Simplify by combining like terms. 4x + 14x<sup>2</sup> - 9x - 5x<sup>2</sup>
A) -9x<sup>2 </sup>- 5x
B) 9x<sup>2</sup> + 5x
C) 9x<sup>2 </sup>- 5x
D) 18x<sup>2 </sup>- 14x
Q2) Determine the product using the product property. (5p<sup>3</sup>q<sup>4</sup>)(p<sup>2</sup>q)
A) 5p<sup>5</sup>q<sup>5</sup>
B) 5p<sup>6</sup>q<sup>4</sup>
C) 5p<sup>5</sup>q<sup>4</sup>
D) 5p<sup>6</sup>q<sup>5</sup>
Q3) Find the binomial square. (4x - 3)<sup>2</sup>
A) 4x<sup>2</sup> - 12x + 9
B) 16x<sup>2</sup> - 12x + 9
C) 16x<sup>2</sup> + 9
D) 16x<sup>2</sup> - 24x + 9
Q4) List all the numbers in the set that are elements of W.
Q5) List all the numbers in the set that are elements of N.
Q6) Factor the difference of perfect squares completely. 9x<sup>2</sup> - 16
Q7) Factor using u-substitution. 36 + x<sup>4</sup> - 13x<sup>2</sup>
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