# c2/c3 inverse trig functions

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#1
Hi,

I've got a problem understanding inverse trig functions. Frequently during c2, I took the inverse of a trig value, and my understanding was that and I thought of this as if we know the sin value (y), if we took the inverse of it, this would give us the angle, x. So, undoing the sin of y, gives x. This makes sense to me.

Now at c3, they say it is . This doesn't make sense to me because the y value on a trig graph has the sin function applied to it, so any y value, say 0.5 is a tig value. I don't understand!
0
6 years ago
#2
The angle of x got nothing to do with the inverse.
0
6 years ago
#3
(Original post by marcsaccount)
Hi,

I've got a problem understanding inverse trig functions. Frequently during c2, I took the inverse of a trig value, and my understanding was that and I thought of this as if we know the sin value (y), if we took the inverse of it, this would give us the angle, x. So, undoing the sin of y, gives x. This makes sense to me.

Now at c3, they say it is . This doesn't make sense to me because the y value on a trig graph has the sin function applied to it, so any y value, say 0.5 is a tig value. I don't understand!
I'm afraid I don't understand but I'm willing to help.
0
6 years ago
#4
(Original post by marcsaccount)
Hi,

I've got a problem understanding inverse trig functions. Frequently during c2, I took the inverse of a trig value, and my understanding was that and I thought of this as if we know the sin value (y), if we took the inverse of it, this would give us the angle, x. So, undoing the sin of y, gives x. This makes sense to me.

Now at c3, they say it is . This doesn't make sense to me because the y value on a trig graph has the sin function applied to it, so any y value, say 0.5 is a tig value. I don't understand!
I'm not quite sure what your confusion is.

You can define a functional relationship between any two variables - e.g. you can say or

As long as you know how to invert a (1-1) function defined between a particular domain and range, that is all you have to worry about.

So and

You have to be careful going in the opposite direction because sin (and cos) are many-to-one so you have to use the principal value when inverting.
0
#5
Thanks for everybody's help and replies.

(Original post by davros)
and
OK, I guess my confusion is because So the inverse is Say if x=45, sinx=y, y would = 0.707 (approx), then it would be the inverse of y that would = x so , not
0
6 years ago
#6
(Original post by marcsaccount)
Thanks for everybody's help and replies.

OK, I guess my confusion is because So the inverse is Say if x=45, sinx=y, y would = 0.707 (approx), then it would be the inverse of y that would = x so , not
Basically, yes.

You have to be careful because multiple angles can give the same sine value, but it's purely conventional that you normally plot y against x and not the other way round!
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#7
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