[tex]sine=\dfrac{opposite}{hypotenuse}\\\\cosine=\dfrac{adjacent}{hypotenuse}\\\\tangent=\dfrac{opposite}{adjacent}\\-----------------------\\\\hypotenuse=AB=10\\\\for\ \angle A:\\opposite=CB=8\\adjacent=AC=6\\\\for\ \angle B:\\opposite=AC=6\\adjacent=CB=8\\----------------------------[/tex]
[tex]\text{Substitute:}\\\\\sin A=\dfrac{8}{10}=\dfrac{8:2}{10:2}=\dfrac{4}{5}\\\\\cos A=\dfrac{6}{10}=\dfrac{6:2}{10:2}=\dfrac{3}{5}\\\\\tan A=\dfrac{8}{6}=\dfrac{8:2}{6:2}=\dfrac{4}{3}\\\\\sin B=\dfrac{6}{10}=\dfrac{6:2}{10:2}=\dfrac{3}{5}\\\\\cos B=\dfrac{8}{10}=\dfrac{8:2}{10:2}=\dfrac{4}{5}\\\\\tan B=\dfrac{6}{8}=\dfrac{6:2}{8:2}=\dfrac{3}{4}[/tex]
[tex]\text{Conclusion:}\\\\\sin A=\cos B\ and\ \cos A=\sin B\ and\ \tan A=\dfrac{1}{\tan B}[/tex]
