IGCSE/GCSE/O & A Level/IB/University Student Forum
Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: cashem'up on May 09, 2010, 05:01:55 am
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question from s06 p1 maths......... i have a doubt the ms gives only two values but i get 4.........
sin 2x + 3cos2x = 0 between 0 and 180 solve....
initially i divided by cos2x to get tan2x=3 and found two values 54.2 and 144.2
but then i did
cos2x(tan2x+3)=0 by taking cos 2x in common then i also get values of 45 and 135 but its not there in the MS........have i done any mistake.........help.
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Divide both sides by cos2x:
Tan2x+3=0
Tan2x=-3
2tanx/1-tan2x=-3
2tanx=-3+3tan2x
3tan2x-2tanx-3=0
Tanx= 1.387, or tanx= -0.720
Therefore, x= 54.2, -35.75
Now use the tan graph or the ASTC rule to find the other angles possible:
X= 54.2, 234.2 -35.75, 144.5
Therefore, x= 54.2, 144.5
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sin2x+3cos2x=0
divide by cos2x u get
tan2x+ 3=0
tan2x=-3
2x= tan-1 (-3)
2x=-71.6
x=-35.5
the range is 0-180
period of a tan curve is pi...in this case pi/2 (since it's tan 2x)
x=-35.5+180 =144.5
x=-35.5+90=54.5
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You use the periodicity method. Quite helpful I must say.
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yup. Faster ;)
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yup. Faster ;)
hey thanks guy nid404 and gladiator......... i did the same as wat nid did ...... by the periodicity method however in the 2nd method i attempted i am getting 4 answers where took cos2x is taken common... how is it wrong......
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can you show how you derived your answer?
I can then help rectify
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Use periodicity when you're PERFECT at using it. Other wise you'll lose track.
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can you show how you derived your answer?
I can then help rectify
see i have
sin 2x + 3cos2x = 0
now if i take cos 2x common then
cos2x(sin2x/cos2x +3)
so cos2x(tan2x+3)=0
now one ans is tan2x= -3 and as u did by the periodicity method above get 2 answers
however another would also be cos2x=0 and so u get 2 more answers 45 and 135...................... would that be correct i dont find nethin wrong in it except the fact that its not in the MS
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wait...how on earth do you get cos2x=0 ?
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He factorised the equation. So now either cos2x=0, or tan2x+3=0
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aaah.....ok..
Should give you the same answer. I'll try
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guyzz....ne solution any idea...........??? ???
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Use my method. Works all the time. Takes time, but it's structured and pretty good.
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ohk....now i realize what's wrong in ur case.
you cannot take cos2x common...
they are 2 separate terms.
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I'm sorry I'll have to disagree with you nid404. But what he did was correct. Nothing wrong in taking cos2x a factor.
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ohk....now i realize what's wrong in ur case.
you cannot take cos2x common...
they are 2 separate terms.
i really dont noe how it could be wrong there...........???......... ??? ??? ??? soz but its okay to take cosx common isnt it.................