Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How To Find Sin β?

  1. Oct 3, 2015 #1
    How do you find the numerical value sin β for the triangle shown on below image?

    I can only find

    ##\tan β = \frac{AB}{BD} = \frac{2x}{3x} = \frac{2}{3} = 0.666666667##

    then

    ##β = \tan^{-1} 0.666666667 = 0.59°##

    then

    ##\sin β = \sin 0.59° = 0.0103##

    Is there another method to find the numerical value of sin β?

    triangle.png
     
  2. jcsd
  3. Oct 3, 2015 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    First of all, tan-1(2/3) ≠ 0.59°

    There are two common angular measures in use: degrees and radians. The calculators we use to compute the trig functions and their inverses need to be set on one measure or the other in order to perform the correct calculation.

    The tangent of a 45° angle = 1, so the angle whose tangent is 2/3 will be closer to 45° than to 0°.

    The Pythagorean Identity, sin2(θ) + cos2(θ) = 1, can be manipulated to give

    tan2(θ) + 1 = sec2(θ) or
    cot2(θ) + 1 = csc2(θ),

    where
    csc(θ) = 1 / sin(θ)
    sec(θ) = 1 / cos(θ)
    cot(θ) = 1 / tan(θ)
     
  4. Oct 3, 2015 #3
    You can use the pythagorean theorem in triangle ABD to find y with respect to x and then find sin beta
     
  5. Oct 3, 2015 #4
    From the pythagorean formula, I get:

    ##y^2 = (2x)^2 + (3x)^2##
    ##y^2 = 4x^2 + 9x^2##
    ##y^2 = 13x^2##
    ##y = \sqrt{13x^2}##
    ##y = \sqrt{13}x##

    ##\sin β = \frac{2x}{\sqrt{13}x} = \frac{2}{\sqrt{13}} = \frac{2}{\sqrt{13}} × \frac{\sqrt{13}}{\sqrt{13}} = \frac{2\sqrt{13}}{13}##

    Is that correct?
     
  6. Oct 3, 2015 #5
    That is correct.

    You can even use a calculator to tally.

    atan(2/3) = 33 degrees (approximately)

    sin(33) = 0.546 = 2 / sqrt(13)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How To Find Sin β?
Loading...