Question

Find the value of sec θ for the point (7,6)

Answer 1

`\bf (\stackrel{a}{7}~~,~~\stackrel{b}{6})\impliedby \textit{let's find the hypotenuse first} \\\\\\ \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=√(7^2+6^2)\implies c=√(49+36)\implies \boxed{c=√(85)} \\\\\\ sec(\theta)=\cfrac{hypotenuse}{adjacent}\qquad \qquad sec(\theta )=\cfrac{√(85)}{7}`