How to convert sine transformed vector back to original?

user_2929836 0
Viewed 93

Using R, if I have x <- sin(1:10) Which function do I use to get these values back to 1:10 again?

--Edit--
or better yet, if I have

| a  |   b   | c |
|----|-------|---|
| 1  |  0.84 | ? |
| 2  |  0.91 | ? |
| 3  |  0.14 | ? |
| 4  | -0.76 | ? |
| 5  | -0.96 | ? |
| 6  | -0.28 | ? |
| 7  |  0.66 | ? |
| 8  |  0.99 | ? |
| 9  |  0.41 | ? |
| 10 | -0.54 | ? |

where
a is original values
b is sin(a)

Using a & b and some function, how do I get c to match a again?

transformation trigonometry math r
1 Answers

You cannot. sin is not a one-to-one function; it is periodic. The value b=sin(a)=.84 is shared by an infininte number of potential values of a.

enter image description here

I've plotted points on your values of (a,b) on the graph above. Note that y=.84 (first value) is also consistent with values in the second "hump" (and the third, and fourth, and...but you can't see those in the graph).

user_11298890
Related