Question

Find the point on the terminal side of θ = 3pi/4 that has a y coordinate of 1. Show your work for full credit.

Answer 1

Ok, we know the angle is 3π/4, and that y-coordinate is 1, hmm what's "x"?

$\bf tan(\theta)=\cfrac{y}{x}\qquad tan\left( \frac{3\pi }{4} \right)=\cfrac{1}{x}\implies \cfrac{sin\left( \frac{3\pi }{4} \right)}{cos\left( \frac{3\pi }{4} \right)}=\cfrac{1}{x}\implies \cfrac{\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}}=\cfrac{1}{x} \\\\\\ -1=\cfrac{1}{x}\implies x=-1\qquad \qquad \boxed{(-1,1)}$