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Math Help - Equation Solving

  1. #1
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    Equation Solving

    I'm having difficulty solving this equation and I think I keep going about it wrong.

    Solve the equation cos2x + 2sinx = sin²x in the interval 0≤ x < 360.

    Thanks in advance ^_^
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  2. #2
    Member HappyJoe's Avatar
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    Here's an idea:

    Use cos(2x) = cos^2(x) - sin^2(x), and use cos^2(x) = 1 - sin^2(x) to rewrite the equation into something that involves only sin(x). You should get a quadratic in sin(x), which you can solve with the usual methods.
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  3. #3
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    Thank you ^_^ I didn't realise I could use cos^2(x) = 1 - sin^2(x). I'll have to remember to bear that in mind
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  4. #4
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    Hi,

    I have another question I'm unsure of.

    If f(x) = 2sin(3x - π/2) + 5, what is the range of values of f(x)?

    Thank you again
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  5. #5
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    e^(i*pi)'s Avatar
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    You can tell (either by knowing or looking at the graph) that: -1 \leq \sin(\theta) \leq 1.

    The minimum value of f(x) is f(x) = 2 \cdot -1 + 5. Work out the maximum value and that will give you the range of f(x)
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