Question

find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of negative 1

Answer 1

Check the picture below, is a negative angle, thus, is going "clockwise"

$\bf tan(\theta)=\cfrac{opposite}{adjacent}\qquad tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{x}\implies tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{-1} \\\\\\ -1\cdot tan\left( -\frac{3\pi }{4} \right)=y\implies -1\cdot \cfrac{sin\left( -\frac{3\pi }{4} \right)}{cos\left( -\frac{3\pi }{4} \right)}=y \\\\\\ -1\cdot \cfrac{-1}{-1}=y\implies -1$