Question

Find the exact value of each trig function WITHOUT a calculator.
sin(x-y) if sin x=7/25, cos x=24/25, sin y=3/5 and cos y=4/5

Answer 1

\[ \text{Note: }
\sin(a - b) \equiv \sin(a)\cos(b) - \sin(b)\cos(a) \\

\text{Therefore: }
\sin(x - y) \equiv \sin(x)\cos(y) - \sin(y)\cos(x) \\
\text{Which becomes: } \frac{7}{25} * \frac{4}{5} - \frac{3}{5} * \frac{24}{25} \equiv
-\frac{44}{125}\]