AnswersCREDIT RE-SEAT MNPS Integrated Math III IC S2 26-27The Unit Circle

Solving Trigonometric Equations Answers

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Evaluate: sin–1(1)

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Select all of the following that represent the exact solutions of Sine (x) = StartFraction StartRoot 3 EndRoot Over 2 EndFraction .

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Remember the definition of csc(x).To graph y = csc-1(x) on the calculator, which expression should be typed in the calculator?

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Which is the graph of the inverse secant function?

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Solve: 2sec(x) + 5 = 9Which equation is equivalent to the given equation?

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Solve: 2 cosine (x) + StartRoot 2 EndRoot = 0 for 0 less-than equal to x less-than equal to 2 pi Check all that apply.

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Solve: tan(x) – cos2(x) = sin2(x)

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The motion of a weight that hangs from a spring is represented by the equation h = 8 sine (StartFraction 2 pi over 3 EndFraction t) . It models the weight’s height (in inches) above or below the rest position as a function of time (in seconds). Approximately when will the object be 3 inches above the rest position? Round to the nearest hundredth. seconds

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Answer:

0.18

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Solve 2sin2(x) – 5sin(x) – 3 = 0.Let u = sin(x).Which of the following is equivalent to the given equation?

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(2u + 1)(u – 3) = 0
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(2u + 3)(u – 5) = 0
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(2u – 2)(u – 1) = 0
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Does the equation sin2(x) – 4 = 0 have any solutions? Explain.

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No, the equation has no solutions. Isolating the sine gives sin(x) = ±2. Because the range of sine is [-1, 1], values ±2 are impossible (they are also outside the domain of arcsin). Hence there are no real solutions.

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Which statements did you include in your answer?

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Isolate sin(x) by adding 4 and taking the square root of both sides.
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State that sin(x) = 2 or sin(x) = –2.
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State that –2 and 2 are undefined values of the inverse sine function.
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There are no solutions because –2 and 2 are not in the domain of the function.
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What is the range of y = csc-1(x) ?

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Which are solutions of the given equation?

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What are the solutions to the equation?

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