Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    i am happy with the idea that cos(pi radians) = cos (180 degrees) = -1. however, what about cos(3 + 4j), where j^2 = -1? i suppose it still matters whether the input to the cos function is in degrees or radians in this case, and you can see this by expanding it out. however, is it correct to say 3 + 4j radians/degrees?
    • PS Helper
    Offline

    14
    PS Helper
    When we refer to trigonometric functions with complex arguments, we require the argument to be in radians. 'Radians' doesn't make much sense with complex numbers, but I say it for the following reason.

    For z \in \mathbb{C}, we define \cos z = \displaystyle \sum_{n=0}^{\infty} \dfrac{(-)^{n+1}z^{2n}}{(2n)!} and \sin z = \displaystyle \sum_{n=0}^{\infty} \dfrac{(-)^{n+1}z^{2n+1}}{(2n+1)!} (which is in fitting with the e^{i\theta} = \cos \theta + i\sin \theta identity). This allows us to have all the usual properties of the trig functions defined over the real numbers, but extended to the whole of the complex plane. Using these definitions, we find that \cos \pi = -1 and so on; that is, the argument should be in radians, and so complex arguments correspond to the radians used when working with the reals.

    For anything beyond simple SOH-CAH-TOA stuff, radians should always be used, because the trig functions' useful properties simply don't work if we use degrees, and they don't extend to the complex plane either.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: July 28, 2010

University open days

  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
  • Bournemouth University
    Undergraduate Mini Open Day Undergraduate
    Wed, 9 Jan '19
Poll
Were you ever put in isolation at school?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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.