Question

What is the equation for the inverse of y=1/2 sin x?

Answer 1

swap x and y , and then solve for y
\[ x= \frac{1}{2} \sin y\]

Answer 2

Oh really? That's it?

Answer 3

Technically, y = (1/2)sin(x) does NOT have an inverse function because y = (1/2)sin(x) fails the horizontal line test; also, this should be apparent because sin(x) is periodic.

y = arcsin(x) is not the true inverse of y = sin(x); rather, y = arcsin(x) the inverse of y = sin(x) on the interval [-π/2, π/2], the interval that contains x = 0 and is strictly increasing.

Now, if you want to find the inverse for y = (1/2)sin(x) when x is on [-π/2, π/2], then just switch x and y and re-solve for y. Switching x and y gives:
x = (1/2)sin(y) ==> sin(y) = 2x.

Taking the arcsine of both sides gives:
y = f^-1(x) = arcsin(2x).

Answer 4

So it's basically the same thing I did with something else just like last month x'D Awesomeness

Answer 5

lol

Answer 6

Never realized it was that easy lmao

Answer 7

so you good or another question

Answer 8

Some of this trig stuff I think I just overthink

Answer 9

I'm good for now, if I have another question, I'll open a new post

Answer 10

kk

Answer 11

ty :)