April 18, 2015

Homework Help: Maths- complex numbers

Posted by Jake on Tuesday, February 13, 2007 at 2:45am.

Find tan(3 theta) in terms of tan theta

Use the formula
tan (a + b) = (tan a + tan b)/[1 - tan a tan b)
in two steps. First, let a = b = theta and get a formula for tan (2 theta).
tan (2 theta) = 2 tan theta/[(1 - tan theta)^2]
Then write down the equation for
tan (2 theta + theta)

Are you sure you are supposed to use complex numbers to answer this question? My previous answer used a trigonometric identity. I don't see a way to use complex numbers, but there probably is a way.

Exp(3 i theta) = [Exp(i theta)]^3 --->

cos(3 theta) = c^3 - 3cs^2

sin(3 theta) = 3c^2s - s^3

where c = cos(theta) and s = sin(theta)

This means that:

tan(3 theta) =

[ 3c^2s - s^3]/[c^3 - 3cs^2]

divide numerator and denominator by c^3:

tan(3 theta) =

[ 3t - t^3]/[1 - 3t^2] =

where t = tan(theta)

Thanks everyone for your help. Yes I did have to use complex numbers. Thanks Count I really should have seen your method for myself as I had found cos 3theta and sin 3 theta in an earlier problem.
Thanks again Jake

Answer this Question

First Name:
School Subject:

Related Questions

trig - h t t p : / / i m g 4 0 . i m a g e s h a c k . u s / c o n t e n t . p h...
Trigonometry - Find the exact value of tan(a-b) sin a = 4/5, -3pi/2<a<-pi...
calculus - a billboard 20ft tall is located on top of a building with its lower ...
Trig. - sec^2xcotx-cotx=tanx (1/cos)^2 times (1/tan)-(1/tan)=tan (1/cos^2) times...
Integration - Intergrate sec^3(x) dx could anybody please check this answer. ...
Trig - tan 15 using composite argument? - tan 15 tan (45-30) (tan 45 - tan ...
Math-Trigonometry - Show that if A, B, and C are the angles of an acute triangle...
math - I have a question I have been working on since yesterday and I am not ...
need asap trigg - simplify the expression by using a double angle formula or a ...
calculus - can anyone tell me if tan-1x= 1 over tan x? No. They are different. ...