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Questions and Answers
What is the simplified form of the equation cos(x) cos(2x) + sin(x) sin(2x) over the interval [0, 2π)?
What is the simplified form of the equation cos(x) cos(2x) + sin(x) sin(2x) over the interval [0, 2π)?
Which side of the right triangle is conventionally labeled as 'x' in relation to angle q?
Which side of the right triangle is conventionally labeled as 'x' in relation to angle q?
Based on the Pythagorean Theorem x² + y² = r², which of the following equations accurately relates sec q to tan q?
Based on the Pythagorean Theorem x² + y² = r², which of the following equations accurately relates sec q to tan q?
What value does r represent in the context of the Pythagorean Theorem?
What value does r represent in the context of the Pythagorean Theorem?
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Which trigonometric identity can be used to transform cos(x) cos(2x) + sin(x) sin(2x) into another form?
Which trigonometric identity can be used to transform cos(x) cos(2x) + sin(x) sin(2x) into another form?
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What is required to receive full credit for answers on this exam?
What is required to receive full credit for answers on this exam?
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Which of the following sections does NOT have Eugenia Malitsky as the instructor?
Which of the following sections does NOT have Eugenia Malitsky as the instructor?
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What type of problems does the exam consist of?
What type of problems does the exam consist of?
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Which statement about the use of materials during the exam is incorrect?
Which statement about the use of materials during the exam is incorrect?
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What could result in receiving little or no credit according to the exam guidelines?
What could result in receiving little or no credit according to the exam guidelines?
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What does partial credit depend on for incorrect solutions?
What does partial credit depend on for incorrect solutions?
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What is the maximum total score obtainable on the written problems section of the exam?
What is the maximum total score obtainable on the written problems section of the exam?
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What is emphasized about the organization of work in the exam?
What is emphasized about the organization of work in the exam?
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Which expression is equivalent to $1 - 2 ext{sin}^2 x + ext{sin}^4 x$?
Which expression is equivalent to $1 - 2 ext{sin}^2 x + ext{sin}^4 x$?
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What is the range of solutions for the equation $2 ext{sin}^2 x - 1 = 0$?
What is the range of solutions for the equation $2 ext{sin}^2 x - 1 = 0$?
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For which of the following values of $q$ does the equation $\text{csc} q = 2$ hold true?
For which of the following values of $q$ does the equation $\text{csc} q = 2$ hold true?
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Which of the following is the solution set for $2 ext{sin}^2 x - 1 = 0$ in the interval [0, 2π)?
Which of the following is the solution set for $2 ext{sin}^2 x - 1 = 0$ in the interval [0, 2π)?
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What transformation of the sine function is represented by the equation $\text{csc} q = 2$?
What transformation of the sine function is represented by the equation $\text{csc} q = 2$?
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Which angle is not a solution to the equation $\text{csc} q = 2$?
Which angle is not a solution to the equation $\text{csc} q = 2$?
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What method will give you the solutions to $\text{sin}^4 x + \text{cos}^2 x = 1$?
What method will give you the solutions to $\text{sin}^4 x + \text{cos}^2 x = 1$?
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Which function is used to find the solutions of the equation $2 ext{sin}^2 x - 1 = 0$?
Which function is used to find the solutions of the equation $2 ext{sin}^2 x - 1 = 0$?
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Which transformation correctly describes how g(x) is derived from f(x) given by g(x) = cos(2x p) + 3?
Which transformation correctly describes how g(x) is derived from f(x) given by g(x) = cos(2x p) + 3?
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In which interval does the graph of g(x) contain exactly one period?
In which interval does the graph of g(x) contain exactly one period?
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What is the relationship between the periods of f(x) and g(x)?
What is the relationship between the periods of f(x) and g(x)?
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If g(x) is transformed by shifting f(x) downward p2 units, what will the new function represent?
If g(x) is transformed by shifting f(x) downward p2 units, what will the new function represent?
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What is the equivalent expression for sec(arcsin(2x))?
What is the equivalent expression for sec(arcsin(2x))?
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Which transformation would NOT correctly derive g(x) from f(x)?
Which transformation would NOT correctly derive g(x) from f(x)?
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What does the transformation cos(2x p) imply about the speed of oscillation of g(x)?
What does the transformation cos(2x p) imply about the speed of oscillation of g(x)?
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What does the term 'exactly one period' entail for the function g(x)?
What does the term 'exactly one period' entail for the function g(x)?
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What is the fundamental identity representing the relationship between sine and cosine?
What is the fundamental identity representing the relationship between sine and cosine?
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In a triangle where AB = 8, BC = 7, and AC = 5, which formula is used to find the angle A?
In a triangle where AB = 8, BC = 7, and AC = 5, which formula is used to find the angle A?
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Which of the following is NOT a result of the double angle formulas?
Which of the following is NOT a result of the double angle formulas?
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What does the equation tan²(q) + 1 equal?
What does the equation tan²(q) + 1 equal?
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If cos²(a) + sin²(a) = 1, which of the following conclusions can be drawn?
If cos²(a) + sin²(a) = 1, which of the following conclusions can be drawn?
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Using the law of sines, which quantity can be calculated if the lengths of all three sides of a triangle are known?
Using the law of sines, which quantity can be calculated if the lengths of all three sides of a triangle are known?
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What is the transformed version of cos(2a) according to the identity?
What is the transformed version of cos(2a) according to the identity?
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Which of the following represents the law of cosines?
Which of the following represents the law of cosines?
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What is the radian measure of the central angle for a circle of radius 3 inches and arc length 21 inches?
What is the radian measure of the central angle for a circle of radius 3 inches and arc length 21 inches?
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What is the value of $\cos(\frac{11\pi}{6})$?
What is the value of $\cos(\frac{11\pi}{6})$?
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If $\cos(t) = \frac{5}{6}$, what is $\sin(t + \frac{\pi}{2})$?
If $\cos(t) = \frac{5}{6}$, what is $\sin(t + \frac{\pi}{2})$?
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What is the angle of elevation of the sun if a 5m tall light post casts a shadow of 5√3m?
What is the angle of elevation of the sun if a 5m tall light post casts a shadow of 5√3m?
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What is the exact value of $\cot(q)$ if the terminal side of $q$ lies on the line $3x + 4y = 0$ in the third quadrant?
What is the exact value of $\cot(q)$ if the terminal side of $q$ lies on the line $3x + 4y = 0$ in the third quadrant?
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For the circle with radius r = 3 inches and an arc length of 21 inches, which of the following statements is true?
For the circle with radius r = 3 inches and an arc length of 21 inches, which of the following statements is true?
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What is the principal value of $\sin(\frac{2\pi}{3})$?
What is the principal value of $\sin(\frac{2\pi}{3})$?
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Determine the value of $\sin^2(t) + \cos^2(t)$ based on the given value of $\cos(t) = \frac{5}{6}$.
Determine the value of $\sin^2(t) + \cos^2(t)$ based on the given value of $\cos(t) = \frac{5}{6}$.
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Study Notes
Exam Instructions
- Work through all problems, demonstrating your steps. Lack of work results in no credit.
- Provide clear and detailed explanations for required explanations.
- You do not need to simplify expressions.
- The multiple-choice section is worth 20 points.
- The written section is worth 80 points.
- No textbooks, notes, cell phones, or calculators are permitted during the exam.
- All work must be shown on each problem.
- Organize your work clearly, neatly, and coherently.
- Unsupported answers will not receive full credit.
- Partial credit may be awarded for well-reasoned, but incomplete, solutions.
- Use extra paper if needed, clearly indicating this on the original exam.
Exam Questions (Multiple Choice and Written)
- Expect problems related to finding complements of angles, measuring central angles in circles, finding values of trigonometric functions, and solving trigonometric equations within a specified interval.
- Problems will require the application of trigonometric identities and the Pythagorean theorem.
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Description
Prepare for your upcoming trigonometry exam with these detailed instructions. The exam will cover finding complements of angles, measuring central angles, and solving trigonometric equations. Be sure to show all your work for partial credit and remember that no external resources are permitted.
