P(-5;b) is plotted on the cartesian plane. OP=13 units and R^OP=€

Question

Without a calculator solve: 1) cos€. 2) tan(180°-€)

Comments

You haven’t defined vertex R. Is R the point (-5,0)? 

Answer 1

b is the y-coordinate of P, and since we know OP=13 and the x-coordinate of P is -5, we can work out b=√(13²-(-5)²)=√144=12, making P(-5,12).

However, we are not given the coordinates of R, so let’s assume R(-5,0) making triangle ROP a right triangle. OR=5, PR=12.

(1) From this assumption cosROP=cos€=OR/OP=5/13 as measured in quadrant 2.

(2) tan€=PR/OR=12/5 as measured in quadrant 2. € as measured here is an acute angle (between 0º and 90º), so its supplementary angle 180-€ is obtuse (between 90º and 180º) and tan(180-€)=-tan€=-12/5, because all obtuse angles have a negative tangent.