Understanding sin(-x) | Exploring the Sine Function for Negative Angles in Trigonometry

sin(-x)

The sine function, denoted as sin(x), is a trigonometric function that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse

The sine function, denoted as sin(x), is a trigonometric function that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse. However, in this case, you are looking for sin(-x), which represents the sine of the negative of an angle.

When we consider sin(-x), we can use the concept of the unit circle to find its value. The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane.

If we consider an angle of x in standard position (starting from the positive x-axis and rotating counterclockwise), then the angle -x would be in the opposite direction, or a clockwise rotation.

Since the unit circle is symmetric about the y-axis, the sine value at an angle -x is equal to the negative of the sine value at an angle x. In other words, sin(-x) = -sin(x).

For example, if sin(x) = 0.5, then sin(-x) would be -0.5.

To summarize, sin(-x) is the negative of sin(x) and represents the sine of the negative of an angle.

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