Question

Is sin^(-1)cosx equal to 1?

Answer 1

HI!!

Answer 2

\[\sin^{-1}\cos(x)\]

Answer 3

Hey there!

Answer 4

\[\sin^{-1}(\cos(x))\] like that?

Answer 5

Yeah, that is it. I'm thinking it is one since cos and sin are integrals/derivatives of each other, and they both equal one in the double angle identity

Answer 6

no , pretty sure it is not one

Answer 7

i believe it is some kind of saw tooth function

Answer 8

here is a nice picture
http://www.wolframalpha.com/input/?i=arcsin(cos(x))

Answer 9

mmm, okay. The part where this comes from is this other equation...
\[\int\limits_{cosx}^{0}\frac{ dt }{ \sqrt{1-t^2} }\]

Answer 10

hard to say what it is really \[\sin^{-1}(\cos(0))=\sin^{-1}(1)=\frac{\pi}{2}\]for example

Answer 11

mmm, yeah, I figured. I was trying to see if maybe they would cancel each other in some way through algebra

Answer 12

can you post the entire quesition?

Answer 13

at this point you get exactly what you wrote as an answer, a function, not a number

Answer 14

\[\sin^{-1}(0)-\sin^{-1}(\cos(x))\]

Answer 15

The question is:
Find dy/dx of the following equation:
\[y=\int\limits_{cosx}^{0}\frac{ dt }{ \sqrt{1-t^2} }\]

Answer 16

aka \[-\sin^{-1}(\cos(x))\]

Answer 17

they dont give me much to work with

Answer 18

lol i knew it !!

Answer 19

you are doing too much work

Answer 20

the fundamental theorem of calculus says the derivative of the integral is the integrand

Answer 21

so first is \[\int_0^{\cos(x)}\frac{1}{\sqrt{1-t^2}}dt\]

Answer 22

then replace \*t\) by \(\cos(x)\) and by the chain rule, multiply by the derivative of cosine

Answer 23

oops meant first is \[-\int_0^{\cos(x)}\frac{1}{\sqrt{1-t^2}}dt\]

Answer 24

then the derivative is \[-\frac{1}{\sqrt{1-\cos^2(x)}}\times (-\sin(x))\]

Answer 25

you can clean it up a lot, like get rid of the two minus signs, and replace the denominator by \(|\sin(x)|\)

Answer 26

mmm, okay, thank you very much! I just didn't read the question and went straight into integrating lol. I really appreciate your help!

Answer 27

\[\color\magenta\heartsuit\]