Results 1 to 8 of 8

Math Help - Tangent of...

  1. #1
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Tangent of...

    Tangent of...-sine.jpg Check the image. I know how to get the answer, but when I use the pythagorean theorem for Cosine 22.5 Why is the answer 2+Sqrt2? Why is it a PLUS instead of a minus? Please show me the steps.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Tangent of...

    What you have posted seems incomplete. You have given the value of sin(22.5) and speak of the cosine of this angle, and your topic title is "Tangent of...". What is it you are trying to find or show?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,628
    Thanks
    430

    Re: Tangent of...

    \sin^2\left(\frac{x}{2}\right) = \frac{1 - \cos{x}}{2}

    \cos(45^\circ) = \frac{\sqrt{2}}{2}

    POSITIVE because 22.5^\circ is a quadrant I angle
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Re: Tangent of...

    So when I do Pythagorean: 1 - 2 \sqrt{2} over 2 equals 2- \sqrt{2} over \sqrt{4}, but you're saying its in quadrant one so its automatically 2+ \sqrt{2} over 4???
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,628
    Thanks
    430

    Re: Tangent of...

    \sin^2(22.5) = \frac{1 - \frac{\sqrt{2}}{2}}{2}

    \sin^2(22.5) = \frac{2 - \sqrt{2}}{4}

    \sin(22.5) = \sqrt{\frac{2 - \sqrt{2}}{4}} = \frac{\sqrt{2 - \sqrt{2}}}{2}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Re: Tangent of...

    Yeah my hw says its + sqrt two NOT that answer.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,628
    Thanks
    430

    Re: Tangent of...

    Quote Originally Posted by Eraser147 View Post
    Yeah my hw says its + sqrt two NOT that answer.
    so check it with a calculator ...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Tangent of...

    The image you posted gives the same value for sin(22.5) that skeeter has given. If you are trying to find \cos(22.5^{\circ}) then use:

    \cos^2\left(\frac{45^{\circ}}{2} \right)=\frac{1+\cos(45^{\circ})}{2}

    \cos^2(22.5^{\circ})=\frac{1+\frac{1}{\sqrt{2}}}{2  }=\frac{2+\sqrt{2}}{4}

    \cos(22.5^{\circ})=\frac{\sqrt{2+\sqrt{2}}}{2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 27th 2011, 12:17 PM
  2. Replies: 6
    Last Post: January 12th 2011, 02:38 PM
  3. Replies: 6
    Last Post: April 7th 2010, 02:34 PM
  4. Replies: 3
    Last Post: February 20th 2009, 05:28 AM
  5. tangent sum
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 19th 2006, 12:50 AM

Search Tags


/mathhelpforum @mathhelpforum