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Thread: Approximate values

  1. #1
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    Approximate values

    Find the approximate values of theta between 0 degrees and 360 degrees that make the following equation a true statement:
    cos thetha = -0.36467

    a) Round final answer to the nearest minute
    b) Round final answer to the nearest 10 minute


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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by subzero06 View Post
    Find the approximate values of theta between 0 degrees and 360 degrees that make the following equation a true statement:
    cos thetha = -0.36467

    a) Round final answer to the nearest minute
    b) Round final answer to the nearest 10 minute


    Okay, $\displaystyle cos \theta = -0,36467$

    Let's see where cos is negative.
    That would be the second and third quadrants.

    Now let's calculate a reference angle.

    $\displaystyle x = cos ^{-1} (0,36467)$ Why did I drop the negative? Because we just determined where it will be negative. All we want now is a reference angle, which we will call $\displaystyle x$.

    $\displaystyle x = 68,61272464$

    Now substitute $\displaystyle x$ into the second and third quadrants.

    Quadrant 2:
    $\displaystyle \theta = 180 - x = 111,3872$

    Quadrant 3:
    $\displaystyle \theta = 180 + x = 248,6127$


    I'm sure you can handle the rounding
    Last edited by janvdl; May 4th 2008 at 01:13 PM. Reason: small technical err :D
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  3. #3
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    Quote Originally Posted by janvdl View Post
    Okay, $\displaystyle cos \theta = -0,36467$

    Let's see where cos is negative.
    That would be the second and third quadrants.

    Now let's calculate a reference angle.

    $\displaystyle x = cos ^{-1} (0,36467)$ Why did I drop the negative? Because we just determined where it will be negative. All we want now is a reference angle, which we will call $\displaystyle x$.

    $\displaystyle x = 68,61272464$

    Now substitute $\displaystyle x$ into the second and third quadrants.

    Quadrant 2:
    $\displaystyle \theta = 180 - x = 111,3872$

    Quadrant 3:
    $\displaystyle \theta = 180 + x = 248,6127$


    I'm sure you can handle the rounding
    111 degree 23' 14.191''
    and
    248 degree 36' 45.809''

    correct?
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  4. #4
    Bar0n janvdl's Avatar
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    Quote Originally Posted by subzero06 View Post
    111 degree 23' 14.191''
    and
    248 degree 36' 45.809''

    correct?
    From my calculator:

    $\displaystyle 111,3872 = 111 ^{o} 23' 13.92''$ (Close enough I guess)

    $\displaystyle 248.6127 = 248 ^{o} 36' 45.72''$ (Once again, close enough)
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  5. #5
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    Quote Originally Posted by janvdl View Post
    From my calculator:

    $\displaystyle 111,3872 = 111 ^{o} 23' 13.92''$ (Close enough I guess)

    $\displaystyle 248.6127 = 248 ^{o} 36' 45.72''$ (Once again, close enough)
    yeah,
    so

    a) Round final answer to the nearest minute
    ans: 111 degree 23'
    ans: 248 degree 36'

    b) b) Round final answer to the nearest 10 minute

    ans: 111 degree 20'
    ans: 248 degree 30'
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  6. #6
    Bar0n janvdl's Avatar
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    Quote Originally Posted by subzero06 View Post
    yeah,
    so

    a) Round final answer to the nearest minute
    ans: 111 degree 23'
    ans: 248 degree 36'

    b) b) Round final answer to the nearest 10 minute

    ans: 111 degree 20'
    ans: 248 degree 30'
    Think it would be:

    b) b) Round final answer to the nearest 10 minute

    ans: 111 degree 20'
    ans: 248 degree 40'
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  7. #7
    Moo
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    Quote Originally Posted by subzero06 View Post
    yeah,
    so

    a) Round final answer to the nearest minute
    ans: 111 degree 23'
    ans: 248 degree 36'

    b) b) Round final answer to the nearest 10 minute

    ans: 111 degree 20'
    ans: 248 degree 30'
    36 is nearer to 40 than 30
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  8. #8
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    Quote Originally Posted by Moo View Post
    36 is nearer to 40 than 30
    oh yeah correct! lol

    bcus it higher than 5
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