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
February 26th, 2011, 10:18 PM   #1
Senior Member
 
Joined: Apr 2007

Posts: 2,140
Thanks: 0

Trigonometry

Let a > 0.
If 25x - ax + 12 = 0 has two roots sin 2? and cos 2?, determine the value of a and tan ?.
johnny is offline  
 
February 27th, 2011, 03:10 AM   #2
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,884
Thanks: 1088

Math Focus: Elementary mathematics and beyond
Re: Trigonometry

a = 49/?(2), tan(?) = ?(2) - 1.
greg1313 is offline  
February 27th, 2011, 04:42 PM   #3
Senior Member
 
Joined: Apr 2007

Posts: 2,140
Thanks: 0

The correct answer is a = 35 and tan ? = , ?. Could you post your solution, greg1313?
johnny is offline  
February 27th, 2011, 06:34 PM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 19,952
Thanks: 1842

a/25 = sin 2? + cos 2?, so a/625 = cos 2? + 2sin 2? cos 2? + sin 2? = 1 + 2(12/25) = 49/25.
Hence a = 35.
skipjack is offline  
February 27th, 2011, 11:20 PM   #5
Senior Member
 
Joined: Apr 2007

Posts: 2,140
Thanks: 0

25x - ax + 12 = 0
x - a/25 x + 12/25 = 0
? and ? are roots of x - (? + ?)x + ?? = 0 (? (x - ?)(x - ?) = x - (? + ?)x + ??)
? a/25 = sin 2? + cos 2? and 12/25 = sin 2? cos 2?
a/25 = sin 2? + 2sin 2? cos 2? + cos 2? = 1 + 2 12/25 = 1 + 24/25 = 49/25 = 7/5
a/25 = 7/5 = 1/5 7
? a = 25/5 7 = 5 7 = 35
johnny is offline  
February 27th, 2011, 11:34 PM   #6
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,884
Thanks: 1088

Math Focus: Elementary mathematics and beyond
Re: Trigonometry

Quote:
Originally Posted by johnny
Could you post your solution, greg1313?
I made a major boo-boo.

Nice to see it solved.
greg1313 is offline  
March 1st, 2011, 07:58 AM   #7
Global Moderator
 
Joined: Dec 2006

Posts: 19,952
Thanks: 1842

Given the above work, it's straightforward to find tan(?).
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
trigonometry



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Trigonometry alloy Trigonometry 2 October 10th, 2012 03:51 AM
HELP :::::: trigonometry PLEASE hgphtgi Trigonometry 3 October 1st, 2012 11:27 AM
Trigonometry yeoky Trigonometry 2 September 27th, 2012 08:04 PM
Trigonometry Rekooo Algebra 6 December 13th, 2010 04:13 PM
Trigonometry!! puremath Algebra 4 May 30th, 2010 01:26 PM





Copyright © 2018 My Math Forum. All rights reserved.