Find the exact coordinates of the point at 135 degree on a c

Find the exact coordinates of the point at -135 degree on a circle of radius 2 centered at the origin. Enter the exact answer. Use the notation (a, b) to give the point.

Solution

Here theta= -135

that is 360-135=225 degree

Therefore theta=225 degree

And point is (x,y)

where x= r cos theta and y= rsin theta

and r=2

Therefore x=2 cos 225 and y =2 sin 225

x=-1.414 (approximately) and y=-1.414(approximately)

Therefore point is (-1.414,-1.414)

Or in radical form it is (- square root 2, - square root 2)