LaddiusMaximus
  • LaddiusMaximus
cosx/1-sinx -1/cosx = tanx what happens to the 1-sinx? I know 1/cosx becomes sec, but what then?
Mathematics
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schrodinger
  • schrodinger
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amistre64
  • amistre64
it should "post" when you hit "post" .....
anonymous
  • anonymous
flip the order and you will have : -1-sinx/cosx = -1/cosx -sinx/cosx sinx/cosx = tanx so; -1/cosx - tanx = -secx-tanx
anonymous
  • anonymous
I guess

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amistre64
  • amistre64
cos - 1 sin ----- --- = --- is this the equation? 1-sin cos cos
LaddiusMaximus
  • LaddiusMaximus
yes
LaddiusMaximus
  • LaddiusMaximus
would algebra be the first step? common denominators?
amistre64
  • amistre64
give it a shot :)
LaddiusMaximus
  • LaddiusMaximus
I thought at first using the reciprocal identity for the 1/cos
LaddiusMaximus
  • LaddiusMaximus
okay now I have sin^2x/1-sinxcosx
LaddiusMaximus
  • LaddiusMaximus
which then becomes sinx/1-cosx
amistre64
  • amistre64
thinking......(12% loaded)
amistre64
  • amistre64
thinking done... got it :)
amistre64
  • amistre64
get like denoms is good; multiply cos/(1-sin) by (cos/cos) to get what?
amistre64
  • amistre64
and 1/cos get multiplied by (1-sin)/(1-sin) to get??
amistre64
  • amistre64
cos^2 - (1-sin) ------------ right? cos(1-sin)
amistre64
  • amistre64
work the top out to: cos^2 + sin -1 ; cos^2 = 1-sin^2 1-sin^2 + sin - 1 ; 1-1 = 0 sin - sin^2 ; factor out a "sin" sin(1-sin) is the top; cancel out (1-sin) top to bottom to get: sin/cos = tan....TADA!!!
amistre64
  • amistre64
you follow that alright?
LaddiusMaximus
  • LaddiusMaximus
yeah but I ended up with cos^2x-1/1-sinxcosx
LaddiusMaximus
  • LaddiusMaximus
then sin^2x/1-sinxcosx
amistre64
  • amistre64
the bottom aint 1-sincos; its cos(1-sin)
amistre64
  • amistre64
cos cos - (1-sin) -------- ------- right?? cos(1-sin) cos(1-sin)
amistre64
  • amistre64
to get like denoms; you need to multiply each side by a convenient form of (1)
amistre64
  • amistre64
cos/cos = 1 AND (1-sin)/(1-sin) = 1
LaddiusMaximus
  • LaddiusMaximus
ohhhh duh
amistre64
  • amistre64
lol ..... mathmatikers are tricky like that :)
LaddiusMaximus
  • LaddiusMaximus
then I start canceling out like numbers right?
amistre64
  • amistre64
there some manipulations first.
amistre64
  • amistre64
the bottom is good; so play with the top.
LaddiusMaximus
  • LaddiusMaximus
so cosx cosx - (1-sinx) becomes cos^2x -(1-sinx)
amistre64
  • amistre64
good; now what multiply out the -(1-sin). what do we get?
LaddiusMaximus
  • LaddiusMaximus
1+sinx
amistre64
  • amistre64
good; and how can we play with cos^2 to make it in terms of "sin"? what does cos^2 =?
LaddiusMaximus
  • LaddiusMaximus
sin^2x
LaddiusMaximus
  • LaddiusMaximus
pythagorean identity?
amistre64
  • amistre64
close.... yes, pyth identity. sin^2 + cos^2 = 1 solve for cos^2, what do we get? subtract sin^2 from each side: cos^2 = 1-sin^2
amistre64
  • amistre64
our top becomes what with this information?
LaddiusMaximus
  • LaddiusMaximus
1-sin^2x-1+sinx
amistre64
  • amistre64
not ..... -1+sin. remember we already took care of that part. It was equal to: +1+sin do you see that? do you understand how we did it?
LaddiusMaximus
  • LaddiusMaximus
but I thought -(1-sinx) would become -1+sinx - times one is -1 and - times -sinx would become +sinx
anonymous
  • anonymous
lol. now I'm lost ._.
amistre64
  • amistre64
you know what.... YOU are correct. I was wrong.... carry on please :)
anonymous
  • anonymous
who?
amistre64
  • amistre64
Laddi was right. And im glad Laddi caught it; have confidence in yourself :)
anonymous
  • anonymous
sorry for the wrong answer laddi!
amistre64
  • amistre64
1-sin^2-1+sin what can we do with this?
anonymous
  • anonymous
replace 1-sin^2 with cose^2
amistre64
  • amistre64
sst; only if we wanna work backwards... lets try to work forwards :)
anonymous
  • anonymous
but why?
LaddiusMaximus
  • LaddiusMaximus
does it become sinx?
amistre64
  • amistre64
lets rewrite it this way: 1-1+sin-sin^2 now what do we do?
LaddiusMaximus
  • LaddiusMaximus
well 1-1 becomes 0, so sin-sin^2 is left.
amistre64
  • amistre64
very good; how can we work this? can we factor anything out to make it look more like the bottom of the fraction? remember the bottom looks like this: cos(1-sin)
amistre64
  • amistre64
think of the top as: x-x^2 if it helps
LaddiusMaximus
  • LaddiusMaximus
sinx can factor out 1-sinx
anonymous
  • anonymous
why don't you just flip cos/1-sin so it will be -(1-sin)/cos?
amistre64
  • amistre64
very good :) that leaves us with: sin(1-sin) sin -------- = --- cos(1-sin) cos can you see that we can do now?
amistre64
  • amistre64
sst; because you change its value if you do that and make a different equation. does 2/x = x/2 for all "x"?
anonymous
  • anonymous
no ofcourse not it's equal to -x/2 ^^
anonymous
  • anonymous
wait, I get what you mean now ^^"
LaddiusMaximus
  • LaddiusMaximus
wait a minute how did (1-sin) get up top? I had sinx+sin^2x
amistre64
  • amistre64
lol .... at least one of us does :)
anonymous
  • anonymous
see, you flipped it!
anonymous
  • anonymous
I knew it
amistre64
  • amistre64
we had: 1-1+sin-sin^2 = sin-sin^2 = sin(1-sin)
myininaya
  • myininaya
find common denominator which you guys did! Good! [ (cosx)^2-1]/[(1-sin(x))(cosx)]
myininaya
  • myininaya
Now 1=(cosx)^2+(sinx)^2
myininaya
  • myininaya
Replace 1 with that
myininaya
  • myininaya
The (cosx)^2 cancel out
anonymous
  • anonymous
there's still more? I thought the question was answered
myininaya
  • myininaya
The nemerator has -(sinx)^2+sinx
LaddiusMaximus
  • LaddiusMaximus
ok confusion. 1-sin^2x-1+sinx becomes what?
amistre64
  • amistre64
myin; your equation is skewed look at what you posted again :)
myininaya
  • myininaya
You can factor out a (sinx) leaving with sinx(-sinx+1)
LaddiusMaximus
  • LaddiusMaximus
sin^2x+sinx
amistre64
  • amistre64
Laddi: (-sin^2) + sin dont forget you (-)
myininaya
  • myininaya
You can do a cancellation leaving you with the desired reult
amistre64
  • amistre64
1 (-)sin^2 (-)1 (+)sin becomes: (-)sin^2 (+)sin
LaddiusMaximus
  • LaddiusMaximus
okay, then what?
myininaya
  • myininaya
Factor out what they have in common which is a sinx
amistre64
  • amistre64
then we factor out a (+sin) to get: sin(1-sin) correct?
LaddiusMaximus
  • LaddiusMaximus
okay so -sinx is left on top?
myininaya
  • myininaya
The numerator gives you sinx(-sinx+1)
anonymous
  • anonymous
no sinx(sinx - 1)
LaddiusMaximus
  • LaddiusMaximus
wait a minute. okay right now I have -sin^2x +sinx/cosx(1-sinx)
myininaya
  • myininaya
No ss the sinx is negative and the 1 is postive
amistre64
  • amistre64
good Laddi;
LaddiusMaximus
  • LaddiusMaximus
so -sin^2x factors out the +sinx?
amistre64
  • amistre64
yes...
LaddiusMaximus
  • LaddiusMaximus
so im left with -sinx/cosx(1-sinx)
myininaya
  • myininaya
You should be left with [(sinx(-sinx+1)]/[cosx(1-sinx)]
myininaya
  • myininaya
Does anything cancel?
amistre64
  • amistre64
(-sin^2 +sin)/cos(1-sin) becomes... sin(1-sin) / cos(1-sin)
anonymous
  • anonymous
I'll just wacth ^-^
myininaya
  • myininaya
-sinx+1=1-sinx So that part in you numerator cancels out with that part in the denominator
amistre64
  • amistre64
Laddi: Does -sin^2 + sin = sin(1-sin) ???
anonymous
  • anonymous
-sin(sin -1)
LaddiusMaximus
  • LaddiusMaximus
I didnt think it did.
anonymous
  • anonymous
or sin(-sin + 1) = sin (1-sin)
anonymous
  • anonymous
^^
anonymous
  • anonymous
lol, yes u were right
LaddiusMaximus
  • LaddiusMaximus
now im confused.
amistre64
  • amistre64
this "find the moving textbox" is rather annoying. They need to find a way to simply "post" your responses without having to play "TAG"
amistre64
  • amistre64
Laddi: lets figure this part out: -sin^2 + sin: can we rewrite this as: sin - sin^2?
anonymous
  • anonymous
don't be confused, now laddi what do you have: -sin^2 + sin right? now take -sin outside, u'll be left with = -sin(sin-1) or you can take sin only outside and u'll be left with sin(-sin + 1) = sin(1-sin) apply the distributive property and you'll get it :)
anonymous
  • anonymous
get it? ^^
amistre64
  • amistre64
sst: one step at a time :)
anonymous
  • anonymous
sorry ^^"
LaddiusMaximus
  • LaddiusMaximus
okay I got that part.
anonymous
  • anonymous
awesome! amistre continue :)
LaddiusMaximus
  • LaddiusMaximus
okay then it becomes 1-sinx?
LaddiusMaximus
  • LaddiusMaximus
that sinx doesnt go away. one takes it place when it factors a sinx out of sin^2x
amistre64
  • amistre64
Laddi; yes
LaddiusMaximus
  • LaddiusMaximus
so sin-sin^2x becomes 1-sinx
amistre64
  • amistre64
it becomes.... pull a sin out...... sin(1-sin) right?
myininaya
  • myininaya
Trig identities are the BEST!
LaddiusMaximus
  • LaddiusMaximus
wait what?
LaddiusMaximus
  • LaddiusMaximus
i thought sinx-sin^2x becomes 1-sinx?
anonymous
  • anonymous
laddi, 4 = 2 x 2 right? let's say we have 4 - 2x, factor what will the answer be?
myininaya
  • myininaya
it becomes sinx(1-sinx)
anonymous
  • anonymous
2(2-x) right?
amistre64
  • amistre64
sin - sin^2. pull out a "sin" put it to the outside... sin (1 - sin) if we multiply it back in we get: sin(1) - sin(sin) = sin - sin^2
anonymous
  • anonymous
imagine the 2 as sinx :)
anonymous
  • anonymous
so instead of 4- 2x we have = 2(2-x) sin^2 - sin = sin(1-sin) ta da!
anonymous
  • anonymous
same story ^^
amistre64
  • amistre64
it is basic algebra... thats all
LaddiusMaximus
  • LaddiusMaximus
havent taken basic algebra in over 10yrs
anonymous
  • anonymous
or or or, sin^2 = sin x sin right? pull one sin outside as a common factor , we're left with sin(1-sin) :)
anonymous
  • anonymous
did u get my example? :)
amistre64
  • amistre64
lol .... it was 20 years for me when I went back to college..
anonymous
  • anonymous
laddi did you understand my example? with the 2 thingy?
LaddiusMaximus
  • LaddiusMaximus
yeah its hard to conceptualize right now.
myininaya
  • myininaya
oh wow i like that word. is that a word conceptualize?
amistre64
  • amistre64
try to recall this: 5a- a^2 = a(5-a)
LaddiusMaximus
  • LaddiusMaximus
hmm I get it now that Im looking at it on paper. sheesh
anonymous
  • anonymous
(sin)(sin) - sin we are going to steal one sin! then...we're left with one sin, soooo, sin(1-sin) to check multiply the (1-sin) with sin , it's going to be equal to ! sin^2-sin! AWESOME!
anonymous
  • anonymous
^_^
amistre64
  • amistre64
paper helps too :)
anonymous
  • anonymous
and a marker
anonymous
  • anonymous
and some juice
anonymous
  • anonymous
and a nap too
anonymous
  • anonymous
good luck laddi hope u got it now :)
amistre64
  • amistre64
nap would be nice :)
myininaya
  • myininaya
More Math!
LaddiusMaximus
  • LaddiusMaximus
so when you take a sin away it becomes 1?
myininaya
  • myininaya
You aren't really taking it away. That 1 is being multiplied by that sinx
LaddiusMaximus
  • LaddiusMaximus
so its more of a standard? 5(a-a^2) becomes 5a-5a^2?

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