Question

which set of rectangular coordinates describes the same location as the polar coordinates 3sqrt2 5pi/4

Answer 1

hello :
note :
rectangular coordinates (x,y)
the polar coordinates (r cosθ , r sinθ )
r= 3√2 and θ = 5π/4
x = r cosθ = 3√2 cos (5π/4) = 3√2 cos(π + π/4)= 3√2 (-cos(π/4))
x =(3√2)(-√2/2)= - 3
y = r sinθ = 3√2 sin (5π/4) = 3√2 sin(π + π/4)= 3√2 (-sin(π/4)) = -3
the rectangular coordinates ( -3 , -3 )