SinX is defined for any angles [0,∞) ?

1. Feb 2, 2012

solve

SinX is defined for any angles [0,∞) ???

1. The problem statement, all variables and given/known data

SinX is defined for any angles [0,∞)

2. Relevant equations

Ok, the domain of sinX is -∞< x < ∞

3. The attempt at a solution

Someone said "You are confused due to fact that Sin(-x)= - sin(x)." Does it mean that just because sinX is not exactly -sinX, sinX will be undefined for all the negative angles since they will produce negative sine function values and we are only interested in positive sine function?

Thanks.

2. Feb 2, 2012

eumyang

Re: SinX is defined for any angles [0,∞) ???

Are you referring to the restricted sine function, "Sin x"? If so, the domain of Sin x isn't [0,∞), but [-π/2, π/2].

3. Feb 2, 2012

solve

Re: SinX is defined for any angles [0,∞) ???

This is from my textbook:

Start with the circle generated by the endpoint A of a straight line OA of unit length rotating anticlockwise about the end O. For angles X where 0<x<pi/2 radians you already know that sinX=AB/AO=AB since AO=1.

That is, the value of the trig ratio sinX is equal to the height of A above B. The sine function with output sinX is now defined as the height of A above B for any angle X (0≤x<∞)

4. Feb 2, 2012

niklaus

Re: SinX is defined for any angles [0,∞) ???

To me it just looks like your textbook is wrong... The sine function is certainly defined for negative angles too (as well as complex numbers, if you know what those are...)

Your statement in 3. makes no sense, since the sine function takes on negative values for some positive x too. But anyway, there are no such restrictions on functions in general, the so-called odd functions (like sin(x)) and even functions (like cos(x)) are special cases. Also, if sin(x) = - sin(x), then sin(x) = 0 ...

5. Feb 2, 2012

solve

Re: SinX is defined for any angles [0,∞) ???

Indeed, sin((3 * pi) / 2) = -1. Weird.

I have to think about how this ties with the rest.

6. Feb 2, 2012

HallsofIvy

Staff Emeritus
Re: SinX is defined for any angles [0,∞) ???

It doesn't. If A= -A, then, adding A to both sides, 2A= 0 so, dividing both sides by 2, A= 0. That has nothing to do with trig functions.