Understanding the Relationship between sin(x) and sin(-x) in Trigonometry

sin(-x)

The expression sin(-x) is the sine function evaluated at the negative of the input x

The expression sin(-x) is the sine function evaluated at the negative of the input x. The sine function is a trigonometric function that gives the ratio of the length of the side opposite to an angle in a right triangle to the length of the hypotenuse.

When we consider the input -x, it means we are looking at the negative value of x in the trigonometric function. The sine function is an odd function, which means it has the property sin(-x) = -sin(x). Therefore, sin(-x) is equal to the negative of sin(x).

In other words, if sin(x) represents the ratio of the length of the opposite side to the hypotenuse for a certain angle x, then sin(-x) represents the same ratio but with a negative sign. The negative sign indicates that the opposite side is in the opposite direction from the original angle x.

It is important to note that the value of sin(-x) can be obtained by evaluating sin(x) and simply changing the sign. So, if you know the value of sin(x) for a given angle x, you can find sin(-x) by taking the negative of that value.

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