Sinx is an odd function.
Explanation
A function is classified as either even, odd, or neither. The classification depends on its symmetry:
- Even Function: A function f(x) is even if f(-x) = f(x) for all x. Even functions are symmetric about the y-axis.
- Odd Function: A function f(x) is odd if f(-x) = -f(x) for all x. Odd functions are symmetric about the origin.
Proof that sin(x) is Odd
To prove that sin(x) is odd, we need to show that sin(-x) = -sin(x). Using the trigonometric identity for the sine of a negative angle:
sin(-x) = -sin(x)
Since this condition is met, sin(x) is an odd function.
Example
Consider x = π/2.
- sin(π/2) = 1
- sin(-π/2) = -1
Therefore, sin(-π/2) = -sin(π/2), which confirms that sin(x) is odd.
