Question

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)

Answer 1

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