Question 1098099
{{{tan(theta)=sin(theta)/cos(theta)}}}
{{{cos(theta)}}}= the x-coordinate of the point {{{P(x,y)}}} where the terminal side of the angle intersects the unit circle.
{{{sin(theta)}}}= the y-coordinate of the point where the terminal side of the angle intersects the unit circle.
In this case, the terminal side crosses the circle of radius 1 at a point with
{{{y<0}}} , but {{{y/x>0}}} , so it must be {{{x<0}}} too.
{{{drawing(300,300,-1.2,1.2,-1.2,1.2,
grid(0),arrow(0,0,-1,-1),
red(circle(0,0,1)),
arc(0,0,0.8,0.8,135,360),
line(-0.283,-0.283,-0.283,-0.233),
line(-0.283,-0.283,-0.333,-0.283),
locate(-0.28,0.283,theta),
circle(-0.707,-0.707,0.02),
locate(-0.72,-0.57,P),
locate(0.3,1.1,quadrant),locate(0.9,1.1,I),
locate(-1,1.1,quadrant),locate(-0.4,1.1,II)
locate(-0.95,-1.05,quadrant),locate(-0.35,-1.05,III),
locate(0.35,-1,quadrant),locate(1,-1,IV)
 )}}} P is in the third quadrant, quadrant III.