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Math Help - More trig trauma!

  1. #1
    Member MathBlaster47's Avatar
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    More trig trauma!

    These questions get nothing but a blank stare from me....kinda irritating really since I sort of like trigonometry.

    Describe each of the following graphs of y. Give (a) its amplitude (if applicable),(b) its maximum and minimum (if applicable) and (c) its period.
    If it has no amplitude, maximum or minimum, write none in the appropriate space.

    1
    y=3\sin\frac{1}{3}x
    (a) 3(I think)

    (b)no idea

    (c) \frac{2\pi}{\frac{1}{3}} (I hope)

    2
    y=\tan 2A

    (a) No clue

    (b) Maximum:none and Minimum: none

    (c) I wish I knew...

    Thank you muchly once again!!
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  2. #2
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    Here's a kick start for the period.

    Period for \sin(bx) is \frac{2\pi}{b}

    Period for \tan(bx) is \frac{\pi}{b}
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  3. #3
    Member MathBlaster47's Avatar
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    Quote Originally Posted by pickslides View Post
    Here's a kick start for the period.

    Period for \sin(bx) is \frac{2\pi}{b}

    Period for \tan(bx) is \frac{\pi}{b}
    Ok....so the period for y=3\sin\frac{1}{3}x is \frac{2\pi}{\frac{1}{3}}

    and the period for [/COLOR][/COLOR] y=\tan 2A is \frac{\pi}{2}?
    Last edited by MathBlaster47; February 5th 2010 at 06:50 AM.
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  4. #4
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    Quote Originally Posted by MathBlaster47 View Post
    These questions get nothing but a blank stare from me....kinda irritating really since I sort of like trigonometry.

    Describe each of the following graphs of y. Give (a) its amplitude (if applicable),(b) its maximum and minimum (if applicable) and (c) its period.
    If it has no amplitude, maximum or minimum, write none in the appropriate space.

    1
    y=3\sin\frac{1}{3}x
    (a) 3(I think)

    (b)no idea

    (c) \frac{2\pi}{\frac{1}{3}} (I hope)

    2
    y=\tan 2A

    (a) No clue

    (b) Maximum:none and Minimum: none

    (c) I wish I knew...

    Thank you muchly once again!!
    #1

    A. amplitude is 3
    B. since graph has no vertical shift and amp is 3, minimum is -3 & max is 3
    c. period is 2pi/b, our b is 1/3 so period is 6pi

    #2

    A. amplitude is understood to be 1
    B. thus, the minimum is -1 and the maximum is 1
    C. period is pi/b, so pi/2
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  5. #5
    Master Of Puppets
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    Quote Originally Posted by MathBlaster47 View Post
    Ok....so the period for y=3\sin\frac{1}{3}x is \frac{2\pi}{\frac{1}{3}}

    and the period for [/color][/color] y=\tan 2A is \frac{\pi}{2}?

    Yep and yep.
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  6. #6
    Member mathemagister's Avatar
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    Hey MathBlaster47! Please keep in mind though, that the amplitude is the absolute value of the coefficient of the trigonometric term.

    So if your first question was y=-3\sin\frac{1}{3}x, the amplitude would still be 3.

    Just keep that in mind, that is a clever little trap that most tests use to catch students off guard. (I've seen this trap in every big trig test I took.)

    Hope that helps you in your future endeavors
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  7. #7
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    Quote Originally Posted by mattio View Post
    #1

    A. amplitude is 3
    B. since graph has no vertical shift and amp is 3, minimum is -3 & max is 3
    c. period is 2pi/b, our b is 1/3 so period is 6pi

    #2

    A. amplitude is understood to be 1 no
    B. thus, the minimum is -1 and the maximum is 1 no
    C. period is pi/b, so pi/2
    the tangent function has no amplitude. it also has no maximum and minimum value since its range is (-\infty , \infty)
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  8. #8
    Member mathemagister's Avatar
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    That is also a good catch, Skeeter. So, to sum up what Skeeter and I have said about amplitudes.

    The amplitude of -3sinx is 3.

    The amplitude of 3cosx is 3.

    The amplitude of -3tanx does not exist.
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