What do you use to find the value of sin(x + y)?

The expression for sin(x + y) is derived from the sine angle addition formula, which states that the sine of the sum of two angles can be calculated using the sines and cosines of the individual angles. Specifically, the formula is sin(x + y) = sin(x)cos(y) + cos(x)sin(y).

This formula arises from the geometric properties of the unit circle and the relationships between the coordinates of points on the circle corresponding to the angles x and y. When you add two angles, the sine of the resulting angle combines the effects of the sine and cosine of both angles.

Therefore, when looking to find the value of sin(x + y), using the sum of the product of the sine and cosine of both angles gives you the correct result. This mathematical principle is fundamental in trigonometry and is widely used in various applications, including physics, engineering, and computer science.

The other options represent different mathematical relationships that do not accurately describe how to compute sin(x + y).