Understanding the Relationship between Sin(x) and Sin(-x): Exploring the Symmetry and Sign Change of Sine Function

sin(-x)

The function sin(x) represents the sine of an angle x

The function sin(x) represents the sine of an angle x. In trigonometry, the sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

However, when we have a negative sign in front of x, such as sin(-x), it affects the sign of the angle and changes the direction.

In general, for any angle θ, sin(-θ) = -sin(θ).

So, sin(-x) = -sin(x).

This means that the sine of a negative angle (-x) is equal to the negative of the sine of the positive angle (x). In other words, the sine function is an odd function, which means it is symmetric about the origin. The graph of sin(-x) is a reflection of the graph of sin(x) across the y-axis.

For example, if sin(x) = 0.5, then sin(-x) = -0.5. The values of sin(x) and sin(-x) have the same magnitude but opposite sign.

In summary, sin(-x) is equal to the negative of sin(x), and it represents the sine of the negative angle (-x).

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