Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

How to get an exact answer instead of a decimal? - Trig+complex no. question in post4

Announcements Posted on
Will you get the grades you need for uni? Get prepared today and de-stress, sign up to email alerts for course places! 02-06-2015
Waiting on IB results? Our IB results hub explains everything you need to know 01-06-2015
  1. Offline

    ReputationRep:
    Hello,

    There's a question from a past papers which wants the answer to be given as an exact value. Answer in mark scheme is 2 + \sqrt{3} and it can be obtained by calculating 2\sqrt{5}[\cos (\pi - \tan^{-1} (0.5) - \frac{2}{3}\pi)]. My calculator gives me the answer in form of 3.732050808. I have no idea how to get it into an exact form...

    ...any help would be appreciated!

    Original question is part (iv) in post#4!
  2. Offline

    ReputationRep:
    That tan^{-1}(0.5) is what's making this hard. Hmm an A level exam asks for this?

    What was the original question?
  3. Offline

    ReputationRep:
    (Original post by Zishi)
    Hello,

    There's a question from a past papers which wants the answer to be given as an exact value. Answer in mark scheme is 2 + \sqrt{3} and it can be obtained by calculating 2\sqrt{5}[\cos (\pi - \tan^{-1} (0.5) - \frac{2}{3}\pi)]. My calculator gives me the answer in form of 3.732050808. I have no idea how to get it into an exact form...

    ...any help would be appreciated!
    Any chance we can see the question? It's possible there's another route ...
  4. Offline

    ReputationRep:
    (Original post by Jam')
    That tan^{-1}(0.5) is what's making this hard. Hmm an A level exam asks for this?

    What was the original question?
    (Original post by ian.slater)
    Any chance we can see the question? It's possible there's another route ...
    Yes, of course there's another route - I did it using an argand diagram(It's a question from Complex Numbers), whereas the mark scheme used 'analogy' from part (ii) to solve part(iv):


    Mark Scheme:


    I now do understand the way mark scheme used, but while solving the question, the only way that popped into my mind was to do it using an argand diagram. But as stated in post#1, that way doesn't give an exact answer....
  5. Offline

    ReputationRep:
    Yes, in general rotating a point by converting to polar coordinates, adding the rotation angle and converting back won't give something that's has an obvious exact form.

    If you desperately wanted to go from your equation involving tan, you could rewrite as cos(t + pi /3), where t=arctan(0.5).

    Tan (pi/3) = sqrt(3), so tan(t+pi/3) = (\sqrt(3)+1/2)/(1-\sqrt{3}/2). Then use cos^2 A = 1/(1+tan^2 A). Wouldn't be a lot of fun, though.
  6. Offline

    ReputationRep:
    (Original post by DFranklin)
    Yes, in general rotating a point by converting to polar coordinates, adding the rotation angle and converting back won't give something that's has an obvious exact form.

    If you desperately wanted to go from your equation involving tan, you could rewrite as cos(t + pi /3), where t=arctan(0.5).

    Tan (pi/3) = sqrt(3), so tan(t+pi/3) = (\sqrt(3)+1/2)/(1-\sqrt{3}/2). Then use cos^2 A = 1/(1+tan^2 A). Wouldn't be a lot of fun, though.
    WOW, I never thought I could use such an easy method. Thanks a lot for it!

Reply

Submit reply

Register

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: March 6, 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

Improving your uni offer

Why now is the time to think about Adjustment

Study resources
x

Think you'll be in clearing or adjustment?

Hear direct from unis that want to talk to you

Get email alerts for university course places that match your subjects and grades. Just let us know what you're studying.

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