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BlingBlong

  • 3 years ago

Solve cos^(2)(x) - 3sin(x) = 3 for x on [0, 2pi] So I have simplified the function down to (-sin(x) - 2)(sin(x) + 1) = 0 or (-sin(x) -1)(sin(x) + 2) = 0 I have determined x = 3pi/2 as sin(3pi/2) = 1/2 Is that the only value possible As I don't think there is a value in the domain of this function that I could use to solve (sin(x) + 2) or (-sin(x) - 2) I could imput arcsin(2) but would that be wrong and if so why?

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  1. watchmath
    • 3 years ago
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    because the value of sin is at most 1. SO arcsin(2) is undefined. So the solutions only comes from -sin x -1 =0

  2. BlingBlong
    • 3 years ago
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    sin(3pi/2) = -1

  3. BlingBlong
    • 3 years ago
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    made a typo. so I'm correct.

  4. watchmath
    • 3 years ago
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    yes \(e\pi/2\) is the only answer

  5. BlingBlong
    • 3 years ago
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    so I should always adhere to the range of the unit circle when dealing with trig functions?

  6. watchmath
    • 3 years ago
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    I mean \(3\pi/2\)

  7. BlingBlong
    • 3 years ago
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    yeah I was wondering lol

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