sarihmanlapaz
If cosA= 15/17 and A is in quadrant III, find cos 1/2A



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AravindG
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ya you have the value of cos A
try to use the formula of cos 2A to get to the answer!!

AravindG
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@sarihmanlapaz did you try that?

sarihmanlapaz
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what will i use in the 3 formula of cos2a?

AravindG
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just look at the equations and look at what we are trying to get the answer in terms of

AravindG
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we want cos A/2 isnt it?

AravindG
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and we have cos A , now you tell me which equation to use!!

sarihmanlapaz
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i think cos^2  1

AravindG
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\[2\cos^2 x1\]

sarihmanlapaz
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so how will i substitute it to that equation?

hartnn
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cosA=2cos^2(A/2)1
find cos(A/2) from here.

AravindG
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@sarihmanlapaz gt it?

sarihmanlapaz
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got it! thanks :)

sarihmanlapaz
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but its none of the choices. >.< how can i solve it?

hartnn
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what did u get ?

sarihmanlapaz
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0.2435

hartnn
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i m getting 0.2435, is that the option ?

sarihmanlapaz
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oh no. haha my answer 0.2435 is in the options. i did'nt notice it.

hartnn
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but A/2 will be in 2nd quadrant where cos is negative.
so we put minus
0.2435

sarihmanlapaz
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its written in the question that the A is in quadrant 3

hartnn
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yes, A in 3rd,A/2 in 2nd.
is 0.2435 in options?

sarihmanlapaz
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the options are. A).0.24054 B).0.24125 C) 0.24254 D) 0.24354

sarihmanlapaz
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pls can you help me?

hartnn
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since all options are positive, i guess A/2 goes in 1st quadrant...then 0.2435 is correct.

sarihmanlapaz
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no. its wrong my friend. i just check the half angle formula. haha there is a formula for cosA/2 = squareroot of 1/2(1+A)

hartnn
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u mean ....(1+cos A) ?

sarihmanlapaz
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yes. yes :) i got the right answer 0.2425

hartnn
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how?
the formula we gave and what u wrote are exactly the same...


sarihmanlapaz
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there is the formula for half angle :)

hartnn
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so using that u got different answer?
we gave u that formula only.....
cosA=2cos^2(A/2)1
so
cos(A/2)=sqrt{0.5*(1+cos A)}

sarihmanlapaz
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yeah. thanks i got the right answer.