Chapter 8.2, Problem 1AYU

The difference formula for the sine function is $\sin \left(A-B\right)=$ _____ . (p.493)

To determine

To find: The difference formula for the sine function is $\text{sin}(\text{A} - \text{B})$ _______________.

Answer to Problem 1AYU

Solution:

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

Explanation of Solution

Given:

To consider any triangle.

Calculation:

Consider any triangle with angles $\text{A,} \text{B}$ and $\text{C}$.

$\text{sin}\left(A - B\right)$ is given by

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