Chapter 10.5, Problem 1AYU

The sum formula for the sine function is $\sin \left(A+B\right)=\_\_\_\_\_\_\_$. (p.493)

To determine

To fill: The sum formula for the sine function $\text{sin}\left(A+B\right)=$ ________________.

Answer to Problem 1AYU

$\sin \left(A+B\right)=\text{ sin}A\text{cos}B+\text{ cos}A\text{sin}B$

Explanation of Solution

Given:

$\text{sin}\left(A+B\right)$

Formula used:

$\cos \left(A-B\right)=\text{ cos}A\text{cos}B+\text{ sin}A\text{sin}B$

Calculation:

$\text{sin}\left(A+B\right)=\cos \left(90-\left(A+B\right)\right)$

$\sin \left(A+B\right)=\cos (\left(90-A\right)-B)$

$\sin \left(A+B\right)=\cos \left(90-A\right)\text{cos}B+\sin \left(90-A\right)\text{sin}B$

$\sin \left(A+B\right)=\text{ sinA cos}B+\text{ cosA sin}B$