Results 1 to 2 of 2

Math Help - really easy trig question

  1. #1
    Newbie
    Joined
    Aug 2005
    Posts
    4

    really easy trig question

    Hi,

    I used to know this, now I can't remember.

    Why is sin (pi/3) (rad) = (root 3)/2

    Michael
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Were you familiar with angles in degrees before? Like 60 degrees is pi/3 radians? Like 30 degrees is pi/6 radians?
    If you were, then, maybe you still recall that:
    "In a 30-60-90-degree right triangle, the leg opposite the 30 degrees is half in measure of the hypotenuse."

    So the 30-60-90 right triangle has these:
    hypotenuse = 2 units
    leg opposite the 30-deg angle = 1 unit

    the other leg, or the leg opposite the 60-deg angle is then sqrt(3) units.
    why? because by Pythagorean theoem,
    (one leg)^2 +(the other leg)^2 = (hypotenuse)^2
    x^2 +1^2 = 2^2
    x^2 +1 = 4
    x^2 = 4 -1
    x^2 = 3
    x = sqrt(3)

    Then, maybe you still know that:
    sine = (opposite side)/(hypotenuse)

    So if the angle is the 60 degrees,
    sin(60deg) = (sqrt(3)) / 2

    Then, since pi/3 rad = 60 deg, it follows that
    sin(pi/3) = (sqrt(3)) / 2

    ------------
    Why is pi/3 rad = 60 degree?

    1 revolution = 360 deg
    1 revolution = 2pi rad also
    So,
    1 rev = 1 rev
    2pi rad = 360 deg
    Divide both sides by 2,
    pi rad = 180 deg
    Divide both sides by 3,
    pi/3 rad = 180/3 deg
    pi/3 rad = 60 deg
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quite an easy trig identity question - need pointers
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: November 14th 2010, 06:55 AM
  2. Easy trig question
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: October 28th 2010, 03:51 PM
  3. easy trig question
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: September 17th 2009, 09:04 AM
  4. Pretty easy trig. question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 20th 2008, 08:22 PM
  5. Quick and easy question trig identities
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: January 12th 2008, 03:37 PM

Search Tags


/mathhelpforum @mathhelpforum