Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    1a)Given that sin(θ+45°) = 2sinθ, show that tanθ = 1÷(2√2-1)

    b) Hence solve the equation sin(θ+45°) = 2sinθ for all values θ between 0° and 360°

    Thanx!!!
    Offline

    15
    ReputationRep:
    (Original post by Looontag)
    1a)Given that sin(θ+45°) = 2sinθ, show that tanθ = 1÷(2√2-1)
    sinθcos45+cosθsin45=2sinθ
    tanθcos45+sin45=2tanθ
    tanθ[cos45-2]=-sin45
    tanθ=(sin45)/(2-cos45)
    tanθ=(0.5rt2)/(2-0.5rt2)
    tanθ=1/(2rt2-1)

    b) Hence solve the equation sin(θ+45°) = 2sinθ for all values θ between 0° and 360°
    tanθ=1/(2rt2-1) so use the cast diagram with your calculator to find all values in the range.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thanks a lot. but where did the tanθcos45°+sin45° = 2tanθ come from???
    Offline

    15
    ReputationRep:
    (Original post by Looontag)
    Thanks a lot. but where did the tanθcos45°+sin45° = 2tanθ come from???
    Dividing through by cosθ as you know sinθ/cosθ=tanθ
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thanks a lot

    (although I do not have a cast diagram on my calculator lol!!)-i presume that is something graphical!!!!

    Thanks again for ur help!
    Offline

    15
    ReputationRep:
    (Original post by Looontag)
    Thanks a lot

    (although I do not have a cast diagram on my calculator lol!!)-i presume that is something graphical!!!!

    Thanks again for ur help!
    Nooo: 'with' your calculator not 'on' your calculator.
    http://www.mathsnet.net/asa2/2004/c24cast.html
    • Thread Starter
    Offline

    0
    ReputationRep:
    Now i feel silly lol.

    I have never heard of the cast diagram before and my exam is tomoro aargh!!! Iv prob learnt some other method of working it out that I can't remember lol.
 
 
 
Turn on thread page Beta
Updated: June 15, 2005
The home of Results and Clearing

1,817

people online now

1,567,000

students helped last year

University open days

  1. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
  2. University of Glasgow
    All Subjects Undergraduate
    Tue, 28 Aug '18
  3. University of Aberdeen
    Undergraduate Open Day Undergraduate
    Tue, 28 Aug '18
Poll
How are you feeling about GCSE results day?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

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