Turn on thread page Beta
    • Thread Starter
    Offline

    2
    ReputationRep:
    how to sketch sin angle +icos angle on an argand diagram?
    Offline

    22
    ReputationRep:
    (Original post by crystalong)
    how to sketch sin angle +icos angle on an argand diagram?
    Mind giving us an example? Just evaluate \sin \alpha - that's your real part and then \cos \alpha that's your imaginary part - from which you should be able to plot it on an argand diagram in the usual way.

    For example: \sin \frac{\pi}{6} + i \cos \frac{\pi}{6} = \frac{1}{2} + i \frac{\sqrt{3}}{2} which you should be able to plot by placing a dot 1/2 a unit along the real axis and rt(3)/2 units up the imaginary axis.
    Offline

    22
    ReputationRep:
    (Original post by Kvothe the arcane)
    Do you mean cos(angle)+isin(angle)?

    Assuming there is no typo, you should know that  sin (angle) +icos (angle) \equiv i(cos(angle)-isin(angle))

    Evaluate cos(angle)-isin(angle) and multiply the complex number by i and you'll be able to plot that in your argand diagram.
    This doesn't make sense, why would he/she do this? Look at my answer.
    • Community Assistant
    • Very Important Poster
    Offline

    20
    ReputationRep:
    Community Assistant
    Very Important Poster
    (Original post by Zacken)
    This doesn't make sense, why would he/she do this? Look at my answer.
    I've deleted my answer. It would have produced the same thing however there were unnecessary steps.
    Offline

    22
    ReputationRep:
    (Original post by Kvothe the arcane)
    I've deleted my answer. It would have produced the same thing however there were unnecessary steps.
    It would have, but it's akin to saying "plot a+ib on an argand diagram, first write this as i(-ai + b), evluate b-ai then multiply it by i then plot it v/s just plot a+ib directly".
    • Community Assistant
    • Very Important Poster
    Offline

    20
    ReputationRep:
    Community Assistant
    Very Important Poster
    (Original post by Zacken)
    It would have, but it's akin to saying "plot a+ib on an argand diagram, first write this as i(-ai + b), evluate b-ai then multiply it by i then plot it v/s just plot a+ib directly".
    I understand . OP, follow Zacken's help above. It'll lead you to the correct answer.
    Offline

    16
    ReputationRep:
    (Original post by crystalong)
    how to sketch sin angle +icos angle on an argand diagram?
    The point lies on a unit circle, inclined at the given angle to the positive x axis
    Offline

    22
    ReputationRep:
    (Original post by ODES_PDES)
    The point lies on a unit circle, inclined at the given angle to the positive x axis
    Read the question again. It's not \cos x + i \sin x.
    • Thread Starter
    Offline

    2
    ReputationRep:
    I mean how to sketch sin theta +icos theta on an argand diagram?
    Offline

    22
    ReputationRep:
    (Original post by Zacken)
    Mind giving us an example? Just evaluate \sin \alpha - that's your real part and then \cos \alpha that's your imaginary part - from which you should be able to plot it on an argand diagram in the usual way.

    For example: \sin \frac{\pi}{6} + i \cos \frac{\pi}{6} = \frac{1}{2} + i \frac{\sqrt{3}}{2} which you should be able to plot by placing a dot 1/2 a unit along the real axis and rt(3)/2 units up the imaginary axis.
    (Original post by crystalong)
    I mean how to sketch sin theta +icos theta on an argand diagram?
    Did you bother reading anything?
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Zacken)
    Did you bother reading anything?
    what if the question states that 0<theta<pie/2 instead of pie/6?
    Offline

    22
    ReputationRep:
    (Original post by crystalong)
    what if the question states that 0<theta<pie/2 instead of pie/6?
    How about you show us the question?
    • Thread Starter
    Offline

    2
    ReputationRep:
    The question is
    Sketch sin theta +icos theta on an argand diagram, where 0<theta<pie/2. find also its modulus and argument.
    Offline

    18
    ReputationRep:
    (Original post by crystalong)
    The question is
    Sketch sin theta +icos theta on an argand diagram, where 0<theta<pie/2. find also its modulus and argument.
    he means do one of these;

    Name:  table.png
Views: 44
Size:  1.6 KB

    also i would suggest drawing it for  \displaystyle  0 &lt; \theta &lt; 2\pi then rubbing out 3/4s of it

    If you do FP2 then you could do like this;


     \displaystyle \text{Let z = complex number (usual notation)}


     \displaystyle   z = \sin\theta + i\cos\theta


     \displaystyle  |z| = |\sin\theta + i\cos\theta|


     \displaystyle  |z| = \sqrt{(\sin\theta)^2 + (\cos\theta)^2}


     \displaystyle  |z| = \sqrt{\sin^2\theta + \cos^2\theta} = \sqrt{1} = 1


     \displaystyle  \therefore |z| = 1

    now its an easy sketch
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by DylanJ42)
    he means do one of these;

    Name:  table.png
Views: 44
Size:  1.6 KB

    also i would suggest drawing it for  \displaystyle  0 &lt; \theta &lt; 2\pi then rubbing out 3/4s of it

    If you do FP2 then you could do like this;


     \displaystyle \text{Let z = complex number (usual notation)}


     \displaystyle   z = \sin\theta + i\cos\theta


     \displaystyle  |z| = |\sin\theta + i\cos\theta|


     \displaystyle  |z| = \sqrt{(\sin\theta)^2 + (\cos\theta)^2}


     \displaystyle  |z| = \sqrt{\sin^2\theta + \cos^2\theta} = \sqrt{1} = 1


     \displaystyle  \therefore |z| = 1

    now its an easy sketch
    I got the modulus part. How do you find the argument?
    Offline

    18
    ReputationRep:
    (Original post by crystalong)
    I got the modulus part. How do you find the argument?
    Yea, that part I have no idea about

    If I was doing it in an exam I would write 0<x<pi/2 because that was the restriction but I'm really not sure
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 16, 2016

2,575

students online now

800,000+

Exam discussions

Find your exam discussion here

Poll
Who is going to be the top scorer of the World Cup in 2018?
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.