Understanding the Unit Circle and the Relationship between sin(-x) and -sin(x)

sin(-x) =

To find the value of sin(-x), let’s first recall the unit circle

To find the value of sin(-x), let’s first recall the unit circle. The unit circle is a circle with a radius of 1, and it is a useful tool for understanding the trigonometric functions.

When we talk about sin(x) on the unit circle, we are referring to the y-coordinate of the point on the circle corresponding to the angle x. Since sin(x) represents the height, it is positive when the angle is in the first and second quadrants, and negative when the angle is in the third and fourth quadrants.

Now, let’s apply this understanding to sin(-x). Since -x is a negative angle, it corresponds to a clockwise rotation on the unit circle. However, the sine function is an odd function, which means sin(-x) = -sin(x), regardless of the value of x.

Therefore, sin(-x) is equal to -sin(x).

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