My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 10th, 2012, 09:59 PM   #1
Senior Member
 
Joined: Apr 2012

Posts: 112
Thanks: 0

Complex numbers: Polar to Cartesian Form

I really need help here!

Using the triple angle identities for sin, cos and tan, Solve the equation
1.) 4x^3 - 3x = -(1/sqrt2)
At first instinct I saw that it resembled the triple angle identity for cosine so I had cos3x=-(1/sqrt2), arccos(1/sqrt2) gave me pi/4 and then cosx is pi/12. However, the answer had cos(11pi/12) and cos(5pi/12), how did they get that?

2.) Solve x^3 - 3sqrt(3)x^2 -3x + sqrt(3) = 0. I couldn't see how it represented any of the triple identities. I thought tan3x is possible but I have problems with the coefficients, they don't tally!

Please help me, thank you so very much!
chocolate is offline  
 
December 11th, 2012, 06:03 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 20,484
Thanks: 2041

(1). Let x = cos(u), then cos(3u) = -1/?2.
Hence 3u = 3?/4 + 2k?, where k is an integer.
Three possibilities are 3u = 3?/4 or -3?/4+2? or 3?/4+2?, giving u = ?/4 or 5?/12 or 11?/12.
Hence x = cos(u) = 1/?2 or 1/(?2 + ?6) or 1/(?2 - ?6).

(2). The equation can be rearranged as (3x - x)/(1 - 3x) = ?3. Let x = tan(u), then tan(3u) = ?3, etc.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
cartesian, complex, form, numbers, polar



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Complex number, Polar to Cartesian form chocolate Algebra 10 November 21st, 2012 10:16 AM
complex numbers---polar form jakeward123 Complex Analysis 5 February 9th, 2011 08:15 AM
How to find polar form and cartesian form of th...... balbasur Algebra 3 July 18th, 2010 06:12 PM
Complex numbers to polar form blackobisk Algebra 1 April 16th, 2009 05:39 PM
Polar to Cartesian Form mathodman Linear Algebra 0 January 5th, 2008 02:01 AM





Copyright © 2019 My Math Forum. All rights reserved.