Question

This is my next Trigonometry question I am needed help on- I just want to be sure I've got it right, or if not, then the steps I need to take to get it right. Thank you.

Answer 1

`\bf \begin{array}{clclll} (-2&,&9)\\ \uparrow &&\uparrow \\ x&&y\\ a&&b \end{array} \\\\\\ c^2=a^2+b^2\implies c=√(a^2+b^2)\implies c=√((-2)^2+(9)^2) \\\\\\ c=√(85)\impliedby \begin{array}{llll} \textit{hypotenuse/radius is just a unit}\\ \textit{thus, is never negative} \end{array} \\\\\\ cos(\theta)=\cfrac{adjacent}{hypotenuse}\implies cos(\theta)=\cfrac{a}{c}\implies cos(\theta)=\cfrac{-2}{√(85)}\\\\ -------------------------------\\\\`


`\bf \textit{now, let's rationalize the denominator} \\\\\\ \cfrac{-2}{√(85)}\cdot \cfrac{√(85)}{√(85)}\implies \cfrac{-2√(85)}{85}`