Results are out! Find what you Get quick advice or join the chat

Unlock these great extras with your FREE membership

  • One-on-one advice about results day and Clearing
  • Free access to our personal statement wizard
  • Customise TSR to suit how you want to use it

A weird trig equation

Announcements Posted on
Rate your uni — help us build a league table based on real student views 19-08-2015
  1. Offline

    (Original post by ztibor)
    THe square of the area
    \displaystyle A^2=\left (\frac{a^2cos \frac{\theta}{2}}{2}\right )^2
    I think you've made an error here and it should be

    \displaystyle A^2=\left (a^2\cos \frac{\theta}{2}\sin \frac{\theta}{2}\right )^2

    Which, once you substitute for "a", is identical to what you get from Heron's formula, so doesn't lead anywhere.
  2. Offline

    By equating two expressions for b from the diagram I arrived at the equation (3+\sqrt{3})\cos \alpha - (3+\sqrt{3})\sin \alpha = (\sqrt{6}+\sqrt{2})\sin \alpha \cos \alpha+(\sqrt{6}-\sqrt{2})\sin^2 \alpha

    where \alpha = \frac{\theta}{2}.

    Then by substituting using t=\tan(\alpha /2 ) you can arrive at a quartic equation in's fairly ugly but like all the other equations, Wolframalpha can solve it and gives t=\sqrt{2}-1 leading to \theta=\frac{\pi}{2}.

    In case any one is interested..
  3. Offline

    Of course, knowing the answer, we could factorise the quartic to arrive at our solution but that's not very satisfying.
  4. Offline

    I did it with vectors. It was probably even more longwinded than BabyMaths effort so I'm not going to bother to post any working.


Submit reply


Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: July 7, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

New on TSR

Rate your uni

Help build a new league table

How do you read?
Study resources
Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.