Need help simplifying trigonometric expression

[Gusty987]

Had this in highly technical...someone said it was "not appropriate" for that forum.

I have the following problem...

cos^2(x)
_______
1+sin(x)

...which I know simplifies to...

1-sin(x)

...I need to know how that was simplified! I will owe a deep debt of gratitude for anyone who can explain this to me!

 

[dighn]

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

 

[Toastedlightly]

doesn't Cos^2 = 1-sin^2?

 

[audi]

i remember doing this last year in precal, i didn't do so hot on the test :Q

 

[Gusty987]

But how do you get around the "+" in the denominator? Could someone explain that in English?

 

[dighn]

Originally posted by: Gusty987
But how do you get around the "+" in the denominator? Could someone explain that in English?

after some manipulation you get: (1+sin)(1-sin)/(1+sin)

(1+sin) is a factor by itself. you don't need to be concerned with the +. you can cancel (1+sin) from both the top and the bottom

 

[audi]

forget me

 

[Gusty987]

you can cancel (1+sin) from both the top and the bottom

I think thats the part I dont get.

 

[audi]

Originally posted by: Gusty987

you can cancel (1+sin) from both the top and the bottom

I think thats the part I dont get.

just think of it as (X*Y)/(x) x will drop out leaving you with just y

 

[dighn]

Originally posted by: Gusty987

you can cancel (1+sin) from both the top and the bottom

I think thats the part I dont get.

well in (1+sin)(1-sin)/(1+sin), on the top level of operations you can see you only have multiplications and divisions. what's inside the parenthesis can be treated as integral parts on this level. so if you set

a = 1+sin
b = 1-sin

you have a*b/a

get it?

 

[Gusty987]

Originally posted by: audi

Originally posted by: Gusty987

you can cancel (1+sin) from both the top and the bottom

I think thats the part I dont get.

just think of it as (X*Y)/(x) x will drop out leaving you with just y

Ok, but how do you get "X" (1+sin x) into the numerator?

get it?

NO!

 

[Gusty987]

Lets look at the fundamentals...

How would you simplify:

x
__

1+y

 

[icejunkie]

or just very simple. lets make (1+sin) = 4, (1-sin) = 3. so you basically get:

4 * 3 / 4 = 12 / 4 = 3.

Now notice, you can cancel out the 4 and the 4, which leaves you with the same thing, 3. (1+sin) in the numerator cancels out with the (1+sin) in the denominator

edit: forget about the X, don't notice it at first. after u get (1+sin)(1-sin)x / (1+sin)x, the (1+sin)x cancels out with the (1+sin)x... leaving u with (1-sin)x...

 

[dighn]

Originally posted by: Gusty987

get it?

NO!

ok..

would you not agree that

(1+x)(1-x)/(1+x) is equivalent to ab/a
if a is (1+x) and b is (1-x)?

then would you not agree that ab/a simplifies to ab/a = b = 1-x?

x
__

1+y

you can't simplify this. at least not if x and y are both variables instead of expressions

 

[icejunkie]

Originally posted by: dighn

Originally posted by: Gusty987

get it?

NO!

ok..

would you not agree that

(1+x)(1-x)/(1+x) is equivalent to ab/a
if a is (1+x) and b is (1-x)?

then would you not agree that ab/a simplifies to ab/a = b = 1-x?

i concur.

 

[Gusty987]

Originally posted by: icejunkie
or just very simple. lets make (1+sin) = 4, (1-sin) = 3. so you basically get:

4 * 3 / 4 = 12 / 4 = 3.

Now notice, you can cancel out the 4 and the 4, which leaves you with the same thing, 3. (1+sin) in the numerator cancels out with the (1+sin) in the denominator

edit: forget about the X, don't notice it at first. after u get (1+sin)(1-sin)x / (1+sin)x, the (1+sin)x cancels out with the (1+sin)x... leaving u with (1-sin)x...

How do you get (1+sin)(1-sin)x from cos^2 x in the numerator?

 

[icejunkie]

Originally posted by: Gusty987

Originally posted by: icejunkie
or just very simple. lets make (1+sin) = 4, (1-sin) = 3. so you basically get:

4 * 3 / 4 = 12 / 4 = 3.

Now notice, you can cancel out the 4 and the 4, which leaves you with the same thing, 3. (1+sin) in the numerator cancels out with the (1+sin) in the denominator

edit: forget about the X, don't notice it at first. after u get (1+sin)(1-sin)x / (1+sin)x, the (1+sin)x cancels out with the (1+sin)x... leaving u with (1-sin)x...

How do you get (1+sin)(1-sin)x from cos^2 x in the numerator?

cos^2 = 1 - sin^2 <-- That's a rule. You SHOULD know that.

1 - sin^2 = (1+sin)(1-sin) <-- simple foiling I think it's called (not good with English math terms)...

do the math man. (1+sin)(1-sin) = 1 - sin + sin -sin^2.... = 1 - sin^s....

 

[Gusty987]

Originally posted by: dighn

Originally posted by: Gusty987

get it?

NO!

ok..

would you not agree that

(1+x)(1-x)/(1+x) is equivalent to ab/a
if a is (1+x) and b is (1-x)?

then would you not agree that ab/a simplifies to ab/a = b = 1-x?

Yes I understand this. The same thing in the numerator and denominator simply cross out. But in the expression I gave, how do you get it into the ab/a form from a/1+b?

 

[icejunkie]

look at my post above.

 

[TuxDave]

If you don't realize that (cosx)^2+(sinx)^2=1... then you need to start paying attention in your trig class.

And if you don't know that x^2-y^2 = (x-y)(x+y)... then you should've paid attention in your algebra class.

 

[Howard]

I wonder how well this guy is doing in his math classes.

 

[Gusty987]

Originally posted by: Howard
I wonder how well this guy is doing in his math classes.

A- last time I checked. Boo ya

 

[audi]

Originally posted by: Gusty987

Originally posted by: Howard
I wonder how well this guy is doing in his math classes.

A- last time I checked. Boo ya

must go to retard school

 

[Gusty987]

Originally posted by: audi

Originally posted by: Gusty987

Originally posted by: Howard
I wonder how well this guy is doing in his math classes.

A- last time I checked. Boo ya

must go to retard school

Texas Tech, actually.

 

[audi]

Originally posted by: Gusty987

Originally posted by: audi

Originally posted by: Gusty987

Originally posted by: Howard
I wonder how well this guy is doing in his math classes.

A- last time I checked. Boo ya

must go to retard school

Texas Tech, actually.

i knew it!