Question

Can anyone help me with this question please? Y=cos^-1(sin x+5).

Answer 1

yeah, forget it. the input is between 4 and 6 and the domain of arccosine is \([0,\pi]\)

Answer 2

you cannot take the inverse cosine of a number larger than \(\pi\) so this does not make sense

Answer 3

ok

Answer 4

in other words
\[\cos^{-1}(\sin(x)+5)\] does not exist
what was the actual question?

Answer 5

it looks like this \[Y=\cos^{-1} (\sin x+5)\]

Answer 6

derive this using the chain rule
\[\frac{ d }{ dx }(\cos^{-1}(\sin(x)+5)=\frac{ -\frac{ du }{ dx } }{ \sqrt{1-u^{2}} }\] where \(u=\sin(x)+5\) and \(\frac{d cos^{-1}(u) }{du}=-\frac{ 1}{ \sqrt{1-u^{2}} }\)

Answer 7

ok

Answer 8

it gives you
\[-\frac{ \frac{ d }{ dx } (\sin(x)+5)}{ \sqrt{1-(\sin(x)+5)^{2}} }\]

Answer 9

then derive each term on the top, then you will get your answer.

Answer 10

can you please help me all the to the answer then I ll work with my other problems too

Answer 11

So this way I ll know the right method to do that

Answer 12

if you dont mind sir?

Answer 13

do you know how to derive sin(x)? and derive 5? because the bottom stays the same and the only thing you need to do is derive sin(x) + 5 on the top

Answer 14

yeah kind of but not sure professor did go over but the way she taught was really confusing

Answer 15

you know the derivative of any number with respect to an unknown, in this case, x, is 0 right?
and then can you derive sin(x) on your own?

Answer 16

hmmm i know that but just to make it sure can you please go over with me to the answer?

Answer 17

the derivative of \(sin (x) \) is \(cos (x) \)

Answer 18

yup

Answer 19

then you have your answer. :)