Is the function p(x) = sinx invertible?

[synkk]

take the function p(x) = sinx

i'm asked to describe the function but I'm not sure what to say as if we take p(90) then we get the value of 1, and if we take p(-90) we get -1, so this would suggest a one-on-one function, but if we take p(360) and p(-360) then the value will be 0 which suggests a many-to-one function,

So which is it?

 

[Simon Bridge]

List the different descriptions/labels available to you and their definitions and you will see.

 

[VantagePoint72]

(In math, we usually express the arguments for trig functions as radians instead of degrees. There's technically nothing wrong with degrees, but you should just know that's how it's usually done. More importantly, if you do use degrees, you need to include the symbol for degrees: sin(90) means the sine of 90 radians, not 90 degrees.)

Look at the plot for sin(x): http://www.wolframalpha.com/input/?i=sin(x) and try to answer to question based on that.

If f(x) = f(y) for even one pair of non-equal numbers x and y then the function cannot be one-to-one. You showed in your question that there is at least one such pair. Just saying that for a single number, f(x) = f(-x) (like you did for 90 degrees) is never enough to conclude that a function is one-to-one, it has to be true for every pair of numbers x,y that f(x) doesn't equal f(y).

 

[synkk]

thanks

 

[AGNuke]

I think you need to determine whether the function is one-one, onto, odd, even, etc.
Hence the function is invertible or not...