Mathematics
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OpenStudy (anonymous):
Math help ! Medals will be given !
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OpenStudy (anonymous):
ok redy
OpenStudy (anonymous):
Simplify the trigonometric expression
OpenStudy (anonymous):
@jim_thompson5910
OpenStudy (anonymous):
how bout me
OpenStudy (anonymous):
What about you ?
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OpenStudy (anonymous):
never mind
OpenStudy (anonymous):
I mean if you can help that will be great if not then move on.
OpenStudy (loser66):
@smartguy1124 help her or not? if you do, i don't.
OpenStudy (anonymous):
@phi
OpenStudy (anonymous):
OK
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jimthompson5910 (jim_thompson5910):
Hints:
sin^2(x) = 1 - cos^2(x)
and
a^2 - b^2 = (a-b)(a+b)
OpenStudy (anonymous):
Is this the formula i will need ?
jimthompson5910 (jim_thompson5910):
yes, you will use this to simplify
OpenStudy (anonymous):
Okay then what ?
jimthompson5910 (jim_thompson5910):
tell me what you get when you use the identity sin^2(x) = 1 - cos^2(x)
then you factor the numerator using a^2 - b^2 = (a-b)(a+b)
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OpenStudy (anonymous):
See this is what i don't understand.
jimthompson5910 (jim_thompson5910):
where are you stuck
OpenStudy (anonymous):
This whole problem.
jimthompson5910 (jim_thompson5910):
well first you replace sin^2(x) with 1 - cos^2(x)
then you factor 1 - cos^2(x) to get ______
OpenStudy (anonymous):
cos^2
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jimthompson5910 (jim_thompson5910):
1 - cos^2(x) is the same as 1^2 - cos^2(x)
now you use the difference of squares factoring rule
OpenStudy (anonymous):
are you asking me or telling me lol
jimthompson5910 (jim_thompson5910):
what do you mean
OpenStudy (anonymous):
Nvm. Was my answer wrong .
jimthompson5910 (jim_thompson5910):
yes 1-cos^2 is not cos^2
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OpenStudy (anonymous):
what is it ?
jimthompson5910 (jim_thompson5910):
do you know what I mean when I say "use the difference of squares rule"?
jimthompson5910 (jim_thompson5910):
if not, then something like 4 - x^2 turns into (2-x)(2+x) using that rule
OpenStudy (anonymous):
okay i seee what your saying. Iv been on this problem for an hour.
jimthompson5910 (jim_thompson5910):
so how does 1 - cos^2(x) factor
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OpenStudy (anonymous):
(2+x)(1-x)
jimthompson5910 (jim_thompson5910):
no (2+x)(1-x) is just an example of how the difference of squares rule works
OpenStudy (anonymous):
This is confusing.
OpenStudy (anonymous):
Okay i looked at it
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jimthompson5910 (jim_thompson5910):
so how would you factor 1 - cos^2(x)
OpenStudy (anonymous):
I didn't see any of those with cos in it only easy numbers.
jimthompson5910 (jim_thompson5910):
ok replace cos(x) with y to make things easier
1 - cos^2(x)
turns into
1-y^2
which factors to ???
OpenStudy (anonymous):
(y+2)(y-2)
jimthompson5910 (jim_thompson5910):
no
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jimthompson5910 (jim_thompson5910):
1-y^2
turns into
1^2-y^2
which factors to ???
OpenStudy (anonymous):
i give up idk
jimthompson5910 (jim_thompson5910):
don't give up
take a break if you must, but definitely don't give up on it
OpenStudy (anonymous):
can we just skip this problem. and move on to another problem.
jimthompson5910 (jim_thompson5910):
ok I'll give you the next step
1 - cos^2(x)
factors to
(1-cos(x))(1+cos(x))
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jimthompson5910 (jim_thompson5910):
I'm sure you see what to do from here
OpenStudy (anonymous):
ok what do i do next.
jimthompson5910 (jim_thompson5910):
well you now have
(1-cos(x))(1+cos(x))
------------------
1-cos(x)
OpenStudy (anonymous):
ok then what ?
jimthompson5910 (jim_thompson5910):
what cancels
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OpenStudy (anonymous):
1-cos?
jimthompson5910 (jim_thompson5910):
yep, leaving you with what
OpenStudy (anonymous):
@satellite73