Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    3
    ReputationRep:
    Hello, this is a really easy question but I'm not sure if I'm working things out correctly here.

    \displaystyle C: r =\sin\theta + \sqrt3\cos\theta, \ 0\leq \theta \leq \frac{\pi}{2}
    At the point P on C, the tangent to C is perpendicular to the initial line. Find the polar coordinates of P.

    Now, what I've done is that

    \displaystyle \text{If the tangent is perpendicular to} \ \theta = 0 \Leftrightarrow \frac{\mathrm{d} x}{\mathrm{d} \theta} = 0

    \displaystyle x = r\cos\theta = \left ( \sin\theta + \sqrt3\cos\theta \right )\cos\theta

    \displaystyle \frac{\mathrm{d} x}{\mathrm{d} \theta} = \cos^{2}\theta - \sin^{2}\theta -2\sqrt3\sin\theta\cos\theta = \cos2\theta - \sqrt3\sin2\theta

    Now, after some simple trig after letting \frac{\mathrm{d} x}{\mathrm{d} \theta} = 0, I've found that \theta = \frac{\pi}{12} and that the required polar coordinates is  \mathrm{P}\left ( \frac{\sqrt{6}+\sqrt{2}}{2}, \frac{\pi}{12} \right ). Can anyone confirm since I don't have the answers to this?
    Offline

    22
    ReputationRep:
    (Original post by aymanzayedmannan)
    Can anyone confirm since I don't have the answers to this?
    Yep, that's fine. :-)
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Zacken)
    Yep, that's fine. :-)
    merci beaucoup, mon ami
    Offline

    19
    ReputationRep:
    am I too late?
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 26, 2016
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
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.