Question

The point (7,7) is a point on the terminal side of theta. What is the exact value of csc theta in simplest form?

Answer 1

`(\stackrel{a}{7}~~,~~\stackrel{b}{7})\qquad \impliedby \textit{let's find its \underline{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=√(7^2+7^2)\implies c=√(7^2(1+1))\implies c=√(7^2(2))\implies c=7√(2) \\\\[-0.35em] ~\dotfill\\\\ csc(\theta )=\cfrac{\stackrel{hypotenuse}{7√(2)}}{\underset{opposite}{7}}\implies csc(\theta )=√(2)`