Question

The point P(8, 6) is on the terminal side of θ. Evaluate sin θ.

Answer 1

`\bf P(\stackrel{a}{8}~,~\stackrel{b}{6})\impliedby \textit{let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=√(a^2+b^2)\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=√(8^2+6^2)\implies c=√(64+36)\implies c=√(100)\implies c=10 \\\\\\ sin(\theta)=\cfrac{\stackrel{b}{opposite}}{\stackrel{c}{hypotenuse}}\implies sin(\theta )=\cfrac{6}{10}\implies sin(\theta )=\cfrac{3}{5}`