Question

What is the value of tanθ when it is at 315 degrees point (√ ̅33,-4)

Answer 1

`\bf \begin{array}{clclll} (√(33)&,&-4)\\ x&&y \end{array}\qquad \qquad tan(\theta)=\cfrac{y}{x}\implies tan(\theta )=\cfrac{-4}{√(3)} \\\\\\ \textit{now, let's rationalize the denominator} \\\\\\ \cfrac{-4}{√(3)}\cdot \cfrac{√(3)}{√(3)}\implies \cfrac{-4√(3)}{(√(3))^2}\implies \boxed{\cfrac{-4√(3)}{3}}`