solve the equation

- anonymous

solve the equation

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- anonymous

sinx=-0.2
on intervals 0

- inkyvoyd

|dw:1378661604837:dw|

- anonymous

how do i solve it algebraically

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## More answers

- inkyvoyd

well as you can see you have two numbers in the locations I've listed. You'll want to take the inverse sine of -0.2

- inkyvoyd

you get -0.20135792079033079145512555221762, or the like. that's saying you're getting|dw:1378661940237:dw| but notice that's notwhat you're looking for

- inkyvoyd

if you add 2pi, notice how you get one answer. I'll leave the second answer to you.

- anonymous

now why do I get that first answer and need to add 2pi

- inkyvoyd

|dw:1378662126741:dw|

- anonymous

no what I mean is why does inverse sin give that. we already review the answer in class and he explained before that something about sin or something yields that answer so to find our answer on the interval we need to add 2pi and then take pi and subtract(add) sin^-1(-.2)

- anonymous

Im just reviewing for the test and I dont remember how to do this one

- inkyvoyd

the reason lies back to what a function and inverse function is

- inkyvoyd

a function is an operation that maps elements of one set onto elements of another set. This relation must be one to one and not one to many, but it can be many to one. However, in the case of a function that has an inverse, it must be a one to one relation. As you can see, while the sine function is definitely many to one, we still define an inverse for it. This isn't a true inverse, but it's useful to what we need. We know that the sine function is a one to one relationship in the domain the inverse sine is defined as.

- inkyvoyd

taking advantage of the periodic nature of the sine function we can then find the answer

- anonymous

so I dont understand the relation of your explanation to the exact reason we add specifcally 2pi

- inkyvoyd

we add 2 pi because the period of the function is 2 pi.

- inkyvoyd

the magic number comes from the fact that the sine function is periodic. there is no true inverse for the sine function, but because it is periodic, we can utilize this to our benefit given that we know the period

- anonymous

Im sorry but I still do not understand

- inkyvoyd

Look, you have to both understand what a function is, what an inverse function is, and what a periodic function is in order to understand why you add 2 pi.

- anonymous

My only guess would be because taking the inverse is like shifting over 2pi so we add 2pi?

- inkyvoyd

a function is an operation that maps elements of one set onto elements of another set. This relation must be one to one and not one to many, but it can be many to one. However, in the case of a function that has an inverse, it must be a one to one relation. As you can see, while the sine function is definitely many to one, we still define an inverse for it. This isn't a true inverse, but it's useful to what we need. We know that the sine function is a one to one relationship in the domain the inverse sine is defined as.
does this make sense to you..

- anonymous

yes

- inkyvoyd

|dw:1378663499375:dw|

- inkyvoyd

|dw:1378663523042:dw| we can find the inverse of the first part but what about the next part?

- anonymous

what do you mean what about the next part?

- inkyvoyd

you are trying to find the inverse function for it.

- inkyvoyd

notice how all the y values are already used up for the inverse, making it a one to many relationship for an inverse function, and that breaks the definition of a function.

- anonymous

ok

- inkyvoyd

because of this we make a funny kludge, and that's where the 2 pi comes from.

- anonymous

ok

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