Nerdgirl
  • Nerdgirl
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)
Mathematics
jamiebookeater
  • jamiebookeater
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alekos
  • alekos
what's another way of writing \[\cos ^{2}\theta\]
Nerdgirl
  • Nerdgirl
cos * cos (theta)?
Nerdgirl
  • Nerdgirl
@alekos

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

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