Question

rewrite the expression so it is not in fractional form sin^2 y/1 − cos y

Answer 1

try multiplying top and bottom by (1+cos y)

Answer 2

I still can't figure this problem out

Answer 3

\[\frac{ \sin^2(y) }{ 1-\cos(y) }\]

Answer 4

what do you get if you multiply the bottom by 1 + cos y ?
(and to keep things kosher, also multiply the top by 1 + cos y )

Answer 5

notice (a-b)(a+b) = a^2 - b^2
is the "short" way to do the multiply

Answer 6

do you get 1 if you multiply them?

Answer 7

no.
do you know FOIL ? that is the long way
(1 - cos y ) ( 1 + cos y)

First
outer
inner
last

Answer 8

oh wow why didn't that come to me the first 50 times I tried this problem?

Answer 9

so then after foiling would I be left with 1-cos^2(y)?

Answer 10

yes,
and there is this *very useful* identity
sin^2 y + cos^2 y = 1
from which we get
sin^2 y = 1 - cos^2 y

Answer 11

Thank you so much!

Answer 12

you should get
\[ \frac{\sin^2 y\ (1+ \cos y)}{\sin^2 y} = 1+\cos y\]

Answer 13

That's exactly what I got, thank you for your help!