Chapter 7.2, Problem 1E

If we know the values of the sine and cosine of x and y, we can find the value of sin(x + y) by using the _____ Formula for Sine. State the formula: sin(x + y) = __________.

To determine

To find: The formula to determine $\sin \left(x+y\right)$, with known values of sine and cosine of x and y.

Answer to Problem 1E

The formula to determine $\sin \left(x+y\right)$ is addition formula for sine function $\sin \left(x+y\right)=\sin x\cos y+\cos x\sin y$.

Explanation of Solution

If the values for sine and cosine functions of x and y are known, $\sin \left(x+y\right)$ can be determined using the addition formula for sine function.

$\sin \left(x+y\right)=\sin x\cos y+\cos x\sin y$

Therefore, if the values of sine and cosine are known then the value of $\sin \left(x+y\right)$ can be determined.