OpenStudy (anonymous):

simplify the trigonometric expression sin^2 theta/1+cos theta

3 years ago
OpenStudy (anteater):

Is there a trig identity you can substitute for sin^2 theta?

3 years ago
OpenStudy (anonymous):

I have no idea what I'm doing. I don't even know what that is.

3 years ago
OpenStudy (anteater):

Are you familiar with sin^2 theta + cos^2 theta = 1?

3 years ago
OpenStudy (anonymous):

No.

3 years ago
OpenStudy (rishavraj):

use sin^theta = 1 - cos^2 theta and after that use rationalisation

3 years ago
OpenStudy (anteater):

Since sin^2 theta + cos^2 theta = 1, then 1 - cos^2 theta = sin^2 theta, so you can substitute

3 years ago
OpenStudy (anteater):

sin^2 theta/(1 + cos theta) = (1-cos^2 theta)/(1 + cos theta)

3 years ago
OpenStudy (anonymous):

I think I might just have to go back and relearn a whole bunch of stuff because I am not understanding any of this

3 years ago
OpenStudy (anteater):

This might help: http://www.intmath.com/trigonometric-functions/2-sin-cos-tan-csc-sec-cot.php

3 years ago
OpenStudy (anteater):

Although I just realized that trig identities are not included there. But this may come in handy: http://www.sosmath.com/trig/Trig5/trig5/trig5.html

3 years ago
OpenStudy (anonymous):

thank you

3 years ago
OpenStudy (anteater):

The link to the first site provides a quick discussion of the different trigonometric ratios (sine, cosine, tangent, cosecant, secant and cotangent).

3 years ago
OpenStudy (anteater):

The second link has useful trig "identities", equivalent expressions that you can substitute for each other

3 years ago
OpenStudy (anteater):

So in the problem you have, you can substitute (1 - cos^2 theta for sin^2 theta). The reason that is useful is because you can then factor 1 - cos^2 theta. 1 - cos^2 theta = (1 + cos theta)(1 - cos theta)

3 years ago
OpenStudy (anteater):

So your expression then becomes (1 + cos theta)(1- cos theta)/(1 + cos theta) The (1 + cos theta) in the numerator and denominator cancel out. And, as rishavraj said, you are left with the answer: 1 - cos theta

3 years ago
OpenStudy (anteater):

So I hope that is somewhat helpful. :)

3 years ago