Question

thanks

Answer 1

switch y and x, and solve for y.

Answer 2

\(\large\color{slate}{ y=1/2~\sin x }\)

switch \(\large\color{slate}{ y}\) and \(\large\color{slate}{ x }\). What do you get after doing so?

Answer 3

x=1/2 sin y ?

Answer 4

yes.

Answer 5

Now, multiply both sides times 2 for me please.

Answer 6

idk wait like what
2/4

Answer 7

\(\large\color{slate}{ x=1/2~\sin (y)~}\)

multiplying both sides times 2 ,

\(\large\color{slate}{ x\color{blue}{\cdot 2}=1/2~\sin (y)~\color{blue}{\cdot 2} }\)

What do you get then?

Answer 8

(what cancels out on the right side ?)

Answer 9

2x=sin(y)?

Answer 10

yes.

Answer 11

now, we know that:

If: \(\large\color{slate}{ \rm{sin{\small~}}(\color{blue}{A})=\color{red}{B} }\)

Then: \(\large\color{slate}{ \rm{Arc{\tiny~}sin{\small~}}(\color{red}{B})=\color{blue}{A} }\)

Answer 12

And so,

If: \(\large\color{slate}{ \rm{sin{\small~}}(\color{blue}{y})=\color{red}{2x} }\)

Then: \(\large\color{slate}{ \rm{Arc{\tiny~}sin{\small~}}(\color{red}{~?~})=\color{blue}{y} }\)

Answer 13

2

Answer 14

2 ?

Answer 15

it would be arcsin(2) ??

Answer 16

or did you mean something else?

Answer 17

y=2 arcsin x?

Answer 18

Again the rule is:
~~~~~~~~~~~~~~~~~~~~~~
If: \(\large\color{slate}{ \rm{sin{\small~}}(\color{blue}{A})=\color{red}{B} }\)

Then: \(\large\color{slate}{ \rm{Arc{\tiny~}sin{\small~}}(\color{red}{B})=\color{blue}{A} }\)

Answer 19

~~~~~~~~~~~~~~~~~~~~~~
If: \(\large\color{slate}{ \rm{sin{\small~}}(\color{blue}{y})=\color{red}{2x} }\)
~~~~~~~~~~~~~~~~~~~~~~

your \(\large\color{slate}{ \rm{{\small~}}\color{blue}{A} }\) is y .
your \(\large\color{slate}{ \rm{{\small~}}\color{red}{B} }\) is 2x .

Answer 20

wait so y=arcsin2x

Answer 21

yes, \(\large\color{slate}{ y={\rm Arcsin}(2x) }\)

Answer 22

\(\large\color{slate}{ \color{blue}{y}={\rm Arcsin}(\color{red}{2x}) }\) see the A and B thingy here?

Answer 23

yes i do thanks so much

Answer 24

You welcome!