Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    need some help on this question, thanks.

    Given that 0º < x < 360º,
    (i) solve 2cos x – sin x = l,
    (ii) deduce the solution set of the inequality
    2cos x – sin x > 1.

    for (i) i got cosx=2/3 so x=48.2 and 228.2, but it seems wrong, so can any1 see what i did wrong?

    for (ii) i comepletely forgot how to do that.
    • PS Reviewer
    Offline

    20
    ReputationRep:
    PS Reviewer
    (Original post by zero334)
    need some help on this question, thanks.

    Given that 0º &lt; x &lt; 360º,
    (i) solve 2cos x – sin x = l,
    (ii) deduce the solution set of the inequality
    2cos x – sin x &gt; 1.

    for (i) i got cosx=2/3 so x=48.2 and 228.2, but it seems wrong, so can any1 see what i did wrong?

    for (ii) i comepletely forgot how to do that.
    For i, you could use Rcos(x+alpha) and then solve for x

    For ii, use a graph once you have your new equation. Then use this information to work out this inequality.
    Offline

    8
    ReputationRep:
    (Original post by zero334)
    need some help on this question, thanks.

    Given that 0º < x < 360º,
    (i) solve 2cos x – sin x = l,
    (ii) deduce the solution set of the inequality
    2cos x – sin x > 1.

    for (i) i got cosx=2/3 so x=48.2 and 228.2, but it seems wrong, so can any1 see what i did wrong?

    for (ii) i comepletely forgot how to do that.
    For (i)
    arrange sinx to the RHS and take square of both side
    4cos^2(x)= 1+2sinx+sin^2(x)
    use that cos^2(x)=1-sin^2(x) this gives a quadratic equation for sinx

    For(ii)
    Use the first quadratic equation to solve the inequality
    Offline

    0
    ReputationRep:
    If you square both sides, always check you don't produce spurious solutions at the end
    Offline

    17
    ReputationRep:
    (Original post by Potassium^2)
    If you square both sides, always check you don't produce spurious solutions at the end
    Thank God someone said it!
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 17, 2011

University open days

  1. University of Edinburgh
    All Departments Undergraduate
    Sat, 22 Sep '18
  2. University of Exeter
    Undergraduate Open Days - Penryn Campus Undergraduate
    Sat, 22 Sep '18
  3. Loughborough University
    General Open Day Undergraduate
    Sat, 22 Sep '18
Poll
Which accompaniment is best?
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.