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March 27, 2017

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Could someone help me with this question

Write in polar form : sinx - i cosx

I've come up to this point, and it's wrong, can't someone please help?

=sin(pie/2-x)-icos(pie/2-x)
=cosx-isinx
=cis(-x)

But the answer is cis(x-pie/2)

  • Maths - ,

    almost

    sinx = cos(pi/2 - x) and cosx = sin(pi/2 - x)
    that is, the sine of any angle equals the cosine of its compliment.

    so sinx - i cosx
    = cos(pi/2 - x) - i sin(pi/2 - x)
    = cis(pi/2 - x)

    this webpage has some good examples with simple diagrams to show your topic

    http://www.intmath.com/Complex-numbers/4_Polar-form.php

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