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Mathematics 69 Online
OpenStudy (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)

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 \[\cos ^{2}\theta = ?\]

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

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

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?

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?

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!

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!!!!!!!!!!!!!

OpenStudy (alekos):

your welcome

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