My Math Forum Simple Trig
 User Name Remember Me? Password

 Algebra Pre-Algebra and Basic Algebra Math Forum

 March 11th, 2011, 03:20 PM #1 Member   Joined: Apr 2010 Posts: 46 Thanks: 1 Simple Trig Simplify the following as much as possible: $\dfrac{cos^3x-3cosxsin^2x}{3sinx-4sin^3x}$ I get that the top simplifies to $sin3x$, but the bottom isn't pretty and I'm not sure what to do with it. Could anyone help me out?
March 11th, 2011, 03:52 PM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: Simple Trig

Hello, clandarkfire!

Quote:
 $\text{Simplify the following as much as possible: }\:\frac{\cos^3\!x\,-\,3\,\!\cos x\,\!\sin^2\!x}{3\,\!\sin x\,-\,4\,\!\sin^3\!x}$

It helps if you know some multiple-angle identities:

[color=beige]. . / / / [/color]$\begin{array}{cccccccccc}\sin\,\!3\!A=&3\,\!\sin A \,-\,4\,\!\sin^3\!A \\ \\ \\ \\ \\ \cos\,\!3\!A=&4\,\!\cos^3\!A\,-\,3\,\!\cos A \end{array}=$

$\text{The numerator is:}$

[color=beige]. . [/color]$\cos^3\!x\,-\,3\,\!\cos x\,\!\sin^2\!x \;=\;\cos^3\!x \,-\,3\,\!\cos x(1\,-\,\cos^2\!x) \;=\;\cos^3\!x\,-\,3\,\!\cos x\,+\,3\,\!\cos^3\!x$

[color=beige]. . . . . . . . . . . . . . . . .[/color]$=\;4\,\!\cos^3\!x\,-\,3\,\!\cos x \;=\;\cos3x$

$\text{The denominator is: }\:3\,\!\sin x \,-\,4\,\!\sin^3\!x \;=\;\sin 3x$

$\text{The problem becomes: }\:\frac{\cos3x}{\sin3x} \;=\;\cot 3x$

 March 11th, 2011, 05:32 PM #3 Member   Joined: Apr 2010 Posts: 46 Thanks: 1 Re: Simple Trig Thankyou! I got the numerator, but my method of finding cos3x gave me $cos3x=cos^3x-cos x sin^2x,$ and somehow I didn't get that that was equal to $3sin x-4sin^3x.$
 March 12th, 2011, 02:51 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,931 Thanks: 2205 If you can't find your mistakes, we can identify them if you post your work here.
 March 12th, 2011, 05:14 PM #5 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 By using the right trigonometric identities, you should be able to arrive at the correct answer.

 Tags simple, trig

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post faiint Trigonometry 5 July 24th, 2012 09:08 AM sparky6 Trigonometry 3 December 19th, 2011 03:08 PM clandarkfire Algebra 4 February 26th, 2011 02:53 AM Aanders5 Algebra 1 March 26th, 2010 02:36 PM wjt Algebra 15 October 26th, 2009 08:31 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top