Question

Can someone verify thisis true? Definition of Sine inverse http://prntscr.com/16145j

Answer 1

hey, friend, it's derivative of sin^-, right?

Answer 2

yeah :)

Answer 3

so, it's "yeah:) " XD

Answer 4

Haha!! i meant yes that is sine inverse that i'm asking about xD

Answer 5

y = Sin^-1(x/a) is equivalent to:

x/a = Sin(y)

Now implicitly differentiate with respect to x:

1/a = Cos(y) (dy/dx)

Answer 6

Hm... i understand what you're doing but i'm trying to understand how cosine ties into this.

Answer 7

dy/dx = 1/(a Cosy)
and then just use some trig and substitution to get to the form that they gave u.

Answer 8

Cos^2 y = 1 - Sin^2 y

Cosy = Sqrt( 1 - Sin^2 y)

Answer 9

lol some ol' trig substitution eh?

Answer 10

x/a = Sin(y), so Sin^2 y = (x/a)^2, so

Cosy = sqrt( 1 - (x/a)^2 )

Answer 11

wait a minute... how did you turn \[\sin^2y \] into \[\cos y\]...

Answer 12

Sin^2 + Cos^2 = 1

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

Answer 13

Oh. derp -_-

Answer 14

And so now you've just proved this formula.

Answer 15

pretty much. Differentiation is easy to prove, integration gets annoying

Answer 16

Yes it does.