Finding coordinates using circles

Question

Find the coordinates of the point at the given angle on a circle of radius 4.2 centered at the origin

(a) −540?

(b) 135?

Answer 1

a)  -540° is 1.5 revolutions around the circle, so it ends on 180°  The coordinates at 180° are (-4.2, 0).

 

b)  135° forms a 45-45-90 triangle in the second quadrant.  The hypotenuse is 4.2, so using the Pythagorean Theorem, we have 

 

x² + x² = (4.2)²

 

2x² = 17.64 (approximately)

 

x^² = 8.82

 

x = 2.97   

 

Both sides of the right triangle are congruent, so the coordinates on the circle are (-2.97, 2.97).

 

Ms. Gayle