# Maths- complex numbers

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

1. 👍 0
2. 👎 0
3. 👁 201

## Similar Questions

1. ### 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 p ? p a g e = d o n e& l = i m g 4 0 / 1 4 8 / a s d a s d y e . j p g & v i a = m u p l o a d (def of tan theta = a^-1 o)a = o opposite = adjacent tan

asked by trig on September 6, 2009
2. ### Math:)

Which trigonometric functions are equivalent to tan(theta)? Select all that apply. (2 answers) a. -tan(-theta)**** b. -tan(theta) c. tan(-theta) d. tan(theta+2pi)**** e. tan(theta+pi/2)

asked by girly girl on March 20, 2018
3. ### calculus

a billboard 20ft tall is located on top of a building with its lower edge 60 ft above the level of a viewers eye. how far from a point directly below the sign should a viewer stand to maximize the angle (theta) between the lines

asked by rachel on November 6, 2011
4. ### Please Check My Work: College Physics

Determine the minimum angle at which a roadbed should be banked so that a car traveling at 20 m/s can safely negotiate the curve if the radius of the curve is 200m. * Data: v=20 m/s r=200m *Formula TAN(theta)=v^2/rg *Solution

asked by Jose Luis on December 3, 2015
5. ### Physics Check My Work Please

Determine the minimum angle at which a roadbed should be banked so that a car traveling at 20 m/s can safely negotiate the curve if the radius of the curve is 200m. * Data: v=20 m/s r=200m *Formula TAN(theta)=v^2/rg *Solution

asked by Jose Luis on December 3, 2015
6. ### science

Sitting on a horizontal track is a mass of 10kg. One end of the track is raised untill the mass just begins to slip. If the coeffieient of static friction is .4 what is the minimum angle at which the mass begins to slip?

asked by Henry on August 24, 2006
7. ### math

I have a question I have been working on since yesterday and I am not making this up. I couldn't get the right answer. If sin theta = -2/3, which of the following are possible? A: cos theta= -the sqr rt of 5/3 and tan theta =2/3.

asked by lisa on November 21, 2013
8. ### Math Trig Help

sin theta = x/3, with theta in the first quadrant, find the expression for cos theta and tan theta. Answers will be in algebraic terms of x. Give exact answers with 0 < theta

asked by Leeroy on November 7, 2014
9. ### Trigonometry

Prove that 1+tan(Theta)/1-tan(Theta) = sec^2(Theta)+2tan(Theta)/1-tan^2(Theta) If you explain, that would be great (:

asked by Marie on August 3, 2012
10. ### Precalc?

Suppose that Cot(theta) = c and 0

asked by Greg on January 23, 2013

More Similar Questions