Results 1 to 5 of 5

Math Help - How to find the value of sin45 degrees?

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    50

    How to find the value of sin45 degrees?

    As far as I know sine has values between 1 and -1 therefore I don't know how to calculate this kind of questions with calculator! Could you help me please...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Feb 2010
    Posts
    50
    Wrong question! Sorry
    Follow Math Help Forum on Facebook and Google+

  3. #3
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    For the record 45 degrees is on the unit circle

    \sin(45) = \dfrac{\sqrt2}{2}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2010
    Posts
    42
    My personal favorite is to do it by the unit circle, File:Unit circle.svg - Wikipedia, the free encyclopedia

    In this particular case, the angle t = 45 degrees, using the notation in the picture.

    Now, we are going to use two basic facts about triangles, the Pythagorean theorem as well as the basic definition of the sine-function. First off, the sum of the angles in a triangle is 180. Meaning that if you know one angle is 90 and one is 45, you know that the third is 180-90-45 = 45 degrees

    Having two equal angles, we know that the two sides not drawn in the picture are the same length. And since we're working in a unit circle, we know that the side drawn, the hypotenuse of the triangle, is 1. Thus, if we call the sides S we know by the Pythagorean theorem that
    S^2 + S^2 = 1
    or
    S = 1/sqrt(2) [sqrt(2) means the square root of two!]

    Now, all we need to do is take the basic definition of the sine-function in a right triangle, that is
    sin(t) = opposite/hypotenuse

    In our case we have sin(45) = (1/sqrt(2))/1 = 1/sqrt(2)

    Hope that helps a little and wasn't just all confusing. My recommendation would be to step back and review the stuff I mentioned in the second paragraph; if you have that down this will be a piece of cake.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,536
    Thanks
    1391
    45 degrees is exactly half of 90 degrees. Since the two non-right angles in a right triangle add to 90 degrees, that means that if one angle is 45 degrees so is the other- a 45, 45, 90 degree triangle is isosceles. If one leg has length, say, 1, so does the other. By the Pythagorean theorem, the length of the hypotenuse, c , is given by c^2= 1^2+ 1^2= 2 so c= \sqrt{2}. Now, sine is "opposite side/hypotenuse" so sin(45)= \frac{1}{\sqrt{2}} and, "rationalizing the denominator, that is \sin(45)= \frac{1}{\sqrt{2}} \frac{\sqrt{2}}{\sqrt{2}}= \frac{\sqrt{2}}{2}.
    Last edited by HallsofIvy; April 5th 2011 at 05:47 AM. Reason: Fixed latex error.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Find the exact value of tan -105 degrees
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: February 28th 2011, 08:14 PM
  2. Find the degrees.
    Posted in the Geometry Forum
    Replies: 4
    Last Post: February 17th 2010, 05:41 AM
  3. find the exact value of cot(795) degrees?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 6th 2009, 01:01 PM
  4. Replies: 2
    Last Post: April 6th 2009, 09:19 AM
  5. cos45=sin45=1/2root2
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 2nd 2009, 07:48 AM

Search Tags


/mathhelpforum @mathhelpforum