|September 28th, 2010, 03:01 AM||#1|
Joined: Sep 2010
Find the solution set please help!
sqrt(3)sin x + cos x =1
Here's what I did,
1. square both sides
3sin^2 x + 2sqrt(3)sin x cos x + cos^2 x = 1
2. expand 3sin^2 x
3-3cos^2 x + 2sqrt(3)sin x cos x + cos^2 x = 1
-2cos^2 x + 2sqrt(3)sin x cos x = -2
4. extract -2cos x
-2cos x (cos x - sqrt(3)sin x) = -2
=> -2cos x = -2
=> cos x = 1
=> 0 deg.
now I'm stopped here,
=> (cos x - sqrt(3)sin x) = -2
And addtl I just want to check my answer in this question,
There is a bike with a pedal and gear measuring 10 radius and 7 radius respectively.
If the bike's wheel(The one in line with the gear; rear wheel) is 42/pi in diameter, how many times the pedal will turn if the bike traveled 60 meters? Put the answer in rev.
Thanks in advance
|September 28th, 2010, 05:12 AM||#2|
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City
Math Focus: Elementary mathematics and beyond
Re: Find the solution set please help!
?(3)sin(x) + cos(x) = 1, cos(x) = 0 is not a solution.
Divide by cos(x):
?(3)tan(x) + 1 = sec(x)
3tanē(x) + 2?(3)tan(x) + 1 = secē(x) = 1 + tanē(x)
2tanē(x) + 2?(3)tan(x) = 0
tanē(x) + ?(3)tan(x) = 0
tan(x)(tan(x) + ?(3)) = 0 ? tan(x) = 0, tan(x) = -?(3) ? x = 0, 2?/3. (? and 5?/3 are not solutions).
|September 29th, 2010, 04:58 AM||#3|
Joined: Dec 2006
The original equation gives (?(3)/2)sin x + (1/2)cos x = 1/2, i.e., sin(x + ?/6) = sin(?/6) = sin(5?/6).
Hence x = 2k? or (2/3)? + 2k?, where k is an integer.
For the 2nd problem, in what units is the wheel's diameter given, and what working was done?
|find, set, solution|
|Search tags for this page|
Click on a term to search for related topics.
|Thread||Thread Starter||Forum||Replies||Last Post|
|find solution of x||Albert.Teng||Algebra||4||February 3rd, 2014 07:36 AM|
|find solution||Albert.Teng||Algebra||2||January 7th, 2014 03:17 AM|
|find solution||D3L3T3||Algebra||4||March 20th, 2012 11:37 AM|
|Find the solution set:||zgonda||Algebra||7||August 23rd, 2010 07:41 PM|
|Can you find the solution?||Mojo||Advanced Statistics||2||October 19th, 2009 08:30 AM|