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Math Help - Graphs of trigonomic functions

  1. #1
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    Graphs of trigonomic functions

    These are problems involving sinusoidal graphs:

    f(x)=-1+4cos\frac{\pi}{3}(x-0.5)

    (a) f(5)
    (b) f(x)=1


    f(t)=50+20cos\frac{2\pi}{6}(x-0.5)

    (a) f(t)=50
    (b) f(40) -- I'm supposed to identify where the sinusoidal graph has a value of 40 at 4 different points.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by uberkrissy View Post
    These are problems involving sinusoidal graphs:

    f(x)=-1+4cos\frac{\pi}{3}(x-0.5)

    (a) f(5)
    (b) f(x)=1


    f(t)=50+20cos\frac{2\pi}{6}(x-0.5)

    (a) f(t)=50
    (b) f(40) -- I'm supposed to identify where the sinusoidal graph has a value of 40 at 4 different points.
    Did you perform the indicated operations? What are you having trouble with here?
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  3. #3
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    I graphed them but I need help finding a and b of each equation.
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  4. #4
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    To find f(5) you just replace "x" with "5" in the formula:
    f(x)=-1+4cos\frac{\pi}{3}(5-0.5)
    That should be easy. You shouldn't even need a calculator.

    The second problem asks you to solve an equation: f(x)=-1+4cos\frac{\pi}{3}(x-0.5)= 1 so add 1 to both sides: 4cos\frac{\pi}{3}(x-0.5)= 2, and then divide both sides by 4: cos\frac{\pi}{3}(x-0.5)= 1/2. Now, for what angles is cosine equal to 1/2?


    For f(t)=50+20cos\frac{2\pi}{6}(x-0.5)= 50 start by subtracting 50 from both sides of the equation.

    I'm not clear on your last question:
    "f(40) -- I'm supposed to identify where the sinusoidal graph has a value of 40 at 4 different points."

    Are you to evaluate f(40), which has a single value, or are you to find 4 different solutions of f(t)= 40?
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