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Math Help - Finding the Linear Speed

  1. #1
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    Finding the Linear Speed

    I just started college trig, I've been looking threw the book but can't find the method to this problem,
    An object is traveling around a circle with a radius of 10 centimeters. If in 20 seconds a central angle of 1/3 radian is swept out, what is the linear speed of the object?
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  2. #2
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    Re: Finding the Linear Speed

    Also, if anyone knows a good place to help me with Trig Identities. I can remember all the identities, I just suck at seeing what to convert them into.
    Just a site for tips and such is what I'm looking for. Thanks.
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  3. #3
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    Re: Finding the Linear Speed

    So it travels 1/3 of a radian in 20 seconds?

    If so its travelling at (1/3)/20 = 1/60 radians per second or one radian per minute.

    Trig identities can be found here: Table of Trigonometric Identities
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  4. #4
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    Re: Finding the Linear Speed

    In case I haven't asked enough already... :P

    Use Fundamental Trig Identities/ Complementary Angle Theorem to find
    If tan^2(theta) = 5, find the exact value of sec^2(theta).
    I tried just makeing a triangle, with sides opposite = 1 and adjacent = 5, giving a hypotenuse of Sqrt26, so Sec would be... sqrt26/5...?
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  5. #5
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    Re: Finding the Linear Speed

    My final answer was 1/6 centimeters/minute... And yet I didn't get that good feeling you get from confidently answering a question...?
    Thanks.

    EDIT: I should have left it at 1/6 centimeters/SECOND, that makes much more sense...
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  6. #6
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    Re: Finding the Linear Speed

    \tan^2\theta = 5

    And

    1+\tan^2\theta = \sec^2\theta

    so  \sec^2\theta = \dots
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  7. #7
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    Re: Finding the Linear Speed

    Quote Originally Posted by Muzik View Post
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    What type of cookies?
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  8. #8
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    Re: Finding the Linear Speed

    Dear pickslides,

    Since 1 radian implies the arc length = radius = 10 cm., can't we say 10 cm. in one minute as the linear speed? I am not clear. Kindly enlighten me. Thanks.
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