Inverse Trig Question: (1 Viewer)

[Fortify]

Prove that:

Sin^-1 x = Cos ^-1 sqrt (1-x^2)

for 0 <= x <= 1

 

[Drongoski]

Prove that:

Sin^-1 x = Cos ^-1 sqrt (1-x^2)

for 0 <= x <= 1

Let sin^-1 x = @

Now draw a right-angled triangle with side = x opp angle @ and hypotenuse = 1

Therefore adjacent side = sqrt(1-x^2)

So cos @ = sqrt(1-x^2)/1 = sqrt(1-x^2)

.: @ = cos^-1 sqrt(1-x^2) = sin^-1 x

QED

 

[gurmies]

Let sin^-1 x = @

Now draw a right-angled triangle with side = x opp angle @ and hypotenuse = 1

Therefore adjacent side = sqrt(1-x^2)

So cos @ = sqrt(1-x^2)/1 = sqrt(1-x^2)

.: @ = cos^-1 sqrt(1-x^2) = sin^-1 x

QED

Hey, i'm curious - is there any other way to do these sorts of questions? The triangle method is easy and all, but I've never seen it done any other way...

 

[jchoi]

You can't, as far as I know because trig is like brothers from another mother.

 

[Fortify]

There's a way to do it, which was the answers in the back of the book.

Let m = sin^-1 x

sin m = x

Now

cos^2 m = 1-sin^2 m

cos^2 m = 1 - x^2

Therefore:

cos m = sqrt (1-x^2)

m = cos^-1 sqrt (1-x^2)

therefore

sin^-1 x = cos^-1 sqrt (1-x^2)

What does QED stand for :S ?

 

[Drongoski]

There's a way to do it, which was the answers in the back of the book.

What does QED stand for :S ?

I think it stands for the Latin: quod erat demonstrandum (But I know no Latin)

We used to say it stands for: Quite Easily Done

 

[jet]

Yeah, it does.
Basically means "that which was meant to be proven"
Though many teachers i know don't like it.

 

[gurmies]

There's a way to do it, which was the answers in the back of the book.

Let m = sin^-1 x

sin m = x

Now

cos^2 m = 1-sin^2 m

cos^2 m = 1 - x^2

Therefore:

cos m = sqrt (1-x^2)

m = cos^-1 sqrt (1-x^2)

therefore

sin^-1 x = cos^-1 sqrt (1-x^2)

What does QED stand for :S ?

Oh, nice =)

 

[shaon0]

There's a way to do it, which was the answers in the back of the book.

Let m = sin^-1 x

sin m = x

Now

cos^2 m = 1-sin^2 m

cos^2 m = 1 - x^2

Therefore:

cos m = sqrt (1-x^2)

m = cos^-1 sqrt (1-x^2)

therefore

sin^-1 x = cos^-1 sqrt (1-x^2)

What does QED stand for :S ?

thats how i usually do it.