Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hiyas, I've done es question, but I'd be really gretful if some1 could check this to see if i've done it right or not. & if i've done it wrong, could i have some pointers plz? =) thanx for yout time!!

    Q) Find the equation of the tangent to the curve y=2sin(x - (pi/6) at the point where x= (pi/3)


    y=2sin(x - (pi/6)
    y= 2 * (sin (x - (pi/6))
    y = 2 (sinxcos(pi/6)) - 2(cosxsin(pi/6))
    y = 2sinx(root3/2) - 2cosx(1/2)
    y = (root3) sinx - cos x


    dy/dx = (root3) cos x + sin x

    At x=(pi/3), y= (root 3)sin(pi/3) - cos(pi/3)
    y= (root 3)(root3/2) - (1/2)
    y= (3/2) - (1/2)
    y= 1

    So point (pi/3, 1) lies on the tangent

    (& Gradient of tangent using derivative)

    dy/dx=(root3) cosx + sin x
    =(root3) cos(pi/3) + sin(pi/3)
    =(root3)(1/2) + (root3/2)
    =(root3/2) + (root3/2)
    =2(root3)/2
    =(root3)


    staight line through (pi/3, 1) & M=(root 3)
    a b

    Eqn of tangent: y-b = m(x-a)
    y - 1 =(root3)(x - (pi/3))
    y - 1= (root3)x -((root3 pi)/3)
    (root3)x -((root3 pi)/3) -y + 1 =0


    Yeah thats what i got, but as I said I'm nae sure..nae any gd at these questions.

    Thanx 4 reading this!! xx
    Offline

    1
    ReputationRep:
    That looks good, but one thing, you don't have to use trig identities to change the orginal function. You can differentiate it straight away, since

    d/dx[2sin(x-(pi/6))] = 2cos(x - (pi/6))

    And continue as normal. Should get the same answer with less work.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thankku! lol, thought no1 would read through it & thanx 4 tha tip! =) xx
 
 
 
Poll
Do you think parents should charge rent?
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.