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
May 14th, 2009, 06:06 AM   #1
Newbie
 
Joined: Jul 2008

Posts: 12
Thanks: 0

Trigonometric equation doesn’t match the graph

Solutions for 2 cos x= tan2x in the domain 0< x< 2pi
Sin2x/cos2x = 2cosx
Sin2x = 2cosx.cos2x
2sinx.cosx - 2cosx (cos^2x – sin^2x) = 0
Cosx (2sinx – 2(cos^2x –sin^2x) = 0
Cosx (2sinx – 2(1 – sin^2x –sin^2x) = 0
Cosx [(2sinx – 2(1 –2sin^2x)] = 0
Cosx (2sinx + 4sin^2x -2) = 0
2Cosx (sinx +2sin^2x -1) = 0



Cosx = o, x = pi/2, 3pi/2
sinx +2sin^2x -1 = 0

sinx =1/2 , x= pi/6, 5pi/6

sinx = -1, x = -pi/2, or 3pi/2

so the solutions are pi/6, 5pi/6, 3pi/2, pi/2

But when we plot 2cosx and tan2x on the same graph they do intersect at six points, and what I am getting are 4 solutions, are there any other solution to this equation.

Shouldn’t the points of intersection indicate that there are six possible solutions to
2 cos x= tan2x
Nazz is offline  
 
May 14th, 2009, 07:28 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 20,753
Thanks: 2136

The graphs have the same slope at x = 3pi/2, so they have a single intersection point there instead of the 4th, 5th and 6th intersection points shown in your diagram.
skipjack is online now  
May 14th, 2009, 07:55 AM   #3
Newbie
 
Joined: Jul 2008

Posts: 12
Thanks: 0

Re: Trigonometric equation doesn’t match the graph

i do agree that the slopes(dy/dx) at 3pi/2 is the same for 2cosx and tanx, but what about the points below and above 3pi/2, aren't they the solutions to 2cosx=tan2x, and if yes then whar are these points
Nazz is offline  
May 14th, 2009, 07:56 AM   #4
Senior Member
 
Joined: Jul 2008

Posts: 895
Thanks: 0

Re: Trigonometric equation doesn’t match the graph

Quote:
Originally Posted by Nazz
But when we plot 2cosx and tan2x on the same graph they do intersect at six points, and what I am getting are 4 solutions, are there any other solution to this equation.
I calculate, and count 4.

[attachment=0:24hvruiu]Trig.jpg[/attachment:24hvruiu]
Dave is offline  
May 14th, 2009, 08:21 AM   #5
Newbie
 
Joined: Jul 2008

Posts: 12
Thanks: 0

Re: Trigonometric equation doesn’t match the graph

thanks dave
Nazz is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
doesn’t, equation, graph, match, trigonometric



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
Trigonometric Equation Help edwinandrew Trigonometry 2 January 15th, 2014 01:29 PM
Match the Parabola HellBunny Algebra 2 March 21st, 2012 09:33 AM
Solution to quadratic equation doesn't look right daigo Algebra 7 February 26th, 2012 11:43 AM
How do you graph trigonometric functions? swish Trigonometry 2 February 9th, 2012 01:24 PM
Match Question sorrry if posted in the wrong section asad_c Abstract Algebra 3 September 1st, 2009 06:49 PM





Copyright © 2019 My Math Forum. All rights reserved.