Trig question please help asap! Fan and medal! :)
Simplify the trigonometric expression.
cos^2 (theta)
-----------
1 - sin (theta)
A. sin (theta)
B. 1 + sin (theta)
C. 1 - sin (theta)
D. 1 - sin (theta)/sin (theta)
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OpenStudy (alekos):
what's another way of writing \[\cos ^{2}\theta\]
OpenStudy (nerdgirl):
cos * cos (theta)?
OpenStudy (nerdgirl):
@alekos
OpenStudy (alekos):
no. use \[\sin ^{2}\theta + \cos ^{2}\theta = 1\]
OpenStudy (alekos):
so \[\cos ^{2}\theta = ?\]
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OpenStudy (nerdgirl):
1 - sin^2 (theta)?
OpenStudy (alekos):
yes thats it, so we now have
\[\frac{ 1-\sin ^{2}\theta }{1-\sin \theta}\]
OpenStudy (alekos):
can you see what we need to do next?
OpenStudy (nerdgirl):
so it would be A?
OpenStudy (alekos):
no not at all
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OpenStudy (alekos):
the numerator can be expressed as the product of two factors
OpenStudy (nerdgirl):
oh oops
OpenStudy (alekos):
any ideas?
OpenStudy (nerdgirl):
I'm thinking that it's either C or D
OpenStudy (alekos):
you're just guessing and not answering my question
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OpenStudy (alekos):
i'm going
OpenStudy (nerdgirl):
i'm going with my gut is what i'm doing.
OpenStudy (nerdgirl):
why are you going?
OpenStudy (alekos):
thats not how you do maths
OpenStudy (alekos):
product of two factors. what do you think?
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OpenStudy (nerdgirl):
Don't go off in a frenzy if I get it wrong but would it (the numerator) be (1 - sin)(sin (theta))?
OpenStudy (alekos):
you're a funny girl. let x = sin(theta)
so we have 1 - x^2
OpenStudy (alekos):
and 1 - x^2 = (1-x)(1+x)
OpenStudy (alekos):
i'm just doing the numerator only
OpenStudy (alekos):
do you follow?
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OpenStudy (nerdgirl):
yes so far
OpenStudy (alekos):
so the numerator is (1-x)(1+x)
and the denominator is 1-x
OpenStudy (alekos):
what can we do now?
OpenStudy (nerdgirl):
so written all out (what you just wrote, just to clarify) it would look like {(1-x)(1+x)}/(1-x)? would the 1-x cancel out?
OpenStudy (alekos):
excellent thats right!
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OpenStudy (alekos):
and we have 1+x
substitute back x = sin(theta)
OpenStudy (alekos):
and the answer is?
OpenStudy (nerdgirl):
B
OpenStudy (alekos):
well done. I hope you now understand how its done?
OpenStudy (nerdgirl):
yes much better :) ty!!!!!!!!!!!!!
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