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Thread: Am I on the right track?

  1. #1
    Member MathBlaster47's Avatar
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    Am I on the right track?

    I have a few questions that I'm pretty sure that I have solved, but need to make sure of:

    Find the exact value of the six trigonometric functions of $\displaystyle \frac{\pi}{4}$ radians.(Leave your answer in radical form.)

    So my answers are:

    $\displaystyle \sin\frac{\pi}{4}=.7104$
    $\displaystyle \cos\frac{\pi}{4}=.7038$
    $\displaystyle \tan\frac{\pi}{4}=1.009$
    $\displaystyle \csc\frac{\pi}{4}=1.408$
    $\displaystyle \sec\frac{\pi}{4}=1.421$
    $\displaystyle \cot\frac{\pi}{4}=.9908$

    I think I got them right, I consulted a table, so I'm just being double sure.

    Thank you!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by MathBlaster47 View Post
    I have a few questions that I'm pretty sure that I have solved, but need to make sure of:

    Find the exact value of the six trigonometric functions of $\displaystyle \frac{\pi}{4}$ radians.(Leave your answer in radical form.)

    So my answers are:

    $\displaystyle \sin\frac{\pi}{4}=.7104$
    $\displaystyle \cos\frac{\pi}{4}=.7038$
    $\displaystyle \tan\frac{\pi}{4}=1.009$
    $\displaystyle \csc\frac{\pi}{4}=1.408$
    $\displaystyle \sec\frac{\pi}{4}=1.421$
    $\displaystyle \cot\frac{\pi}{4}=.9908$

    I think I got them right, I consulted a table, so I'm just being double sure.

    Thank you!
    None of your answers are correct. Exact means exact. All of your answers are approximations.
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  3. #3
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    Sorry I dont think they are...

    $\displaystyle \sin\frac{\pi}{4}=.7104$ that is $\displaystyle \frac{\sqrt2}{2}$
    $\displaystyle \cos\frac{\pi}{4}=.7038$ sin and cosine of $\displaystyle \frac{\pi}{4}$ are equal
    $\displaystyle \tan\frac{\pi}{4}=1.009$ this is exactly 1.000
    $\displaystyle \csc\frac{\pi}{4}=1.408$
    $\displaystyle \sec\frac{\pi}{4}=1.421$
    $\displaystyle \cot\frac{\pi}{4}=.9908$

    Haven´t checked the rest, curious how did you get your answers?
    Hope it helps..
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  4. #4
    Member MathBlaster47's Avatar
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    Well...I cheated a little, you see I consulted a table for my answers as I hadn't the slightest idea how to get my answers.
    How do I work out such a question?
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by MathBlaster47 View Post
    Well...I cheated a little, you see I consulted a table for my answers as I hadn't the slightest idea how to get my answers.
    How do I work out such a question?
    Math Concepts Explained: Special Angles in Trigonometry
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  6. #6
    Member MathBlaster47's Avatar
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    ah....Thank you!
    An explanation I can understand!
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  7. #7
    Member mathemagister's Avatar
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    Quote Originally Posted by MathBlaster47 View Post
    I have a few questions that I'm pretty sure that I have solved, but need to make sure of:

    Find the exact value of the six trigonometric functions of $\displaystyle \frac{\pi}{4}$ radians.(Leave your answer in radical form.)

    So my answers are:

    $\displaystyle \sin\frac{\pi}{4}=.7104$
    $\displaystyle \cos\frac{\pi}{4}=.7038$
    $\displaystyle \tan\frac{\pi}{4}=1.009$
    $\displaystyle \csc\frac{\pi}{4}=1.408$
    $\displaystyle \sec\frac{\pi}{4}=1.421$
    $\displaystyle \cot\frac{\pi}{4}=.9908$

    I think I got them right, I consulted a table, so I'm just being double sure.

    Thank you!
    So just to make sure you got the last three:

    $\displaystyle \csc\frac{\pi}{4}=\frac{1}{sin\frac{\pi}{4}} = \frac{2}{\sqrt2}=\sqrt2$
    $\displaystyle \sec\frac{\pi}{4}=\frac{1}{cos\frac{\pi}{4}} = \frac{2}{\sqrt2}=\sqrt2$
    $\displaystyle \cot\frac{\pi}{4}=\frac{1}{tan\frac{\pi}{4}}=\frac {1}{1} = 1$
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