Question

Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.

(4 square root of 2, 45°), (-4 square root of 2, 225°)
(4 square root of 2, 135°), (-4 square root of 2, 315°)
(4 square root of 2, 225°), (-4 square root of 2, 45°)
(4 square root of 2, 315°), (-4 square root of 2, 135°)

Answer 1

D

Explanation:

`4=r cos \theta\\-4=r sin \theta\\square ~and~add\\16+16=r^2(cos^2 \theta+sin^2\theta)\\r^2=32\\ r=4√(2) \\divide \\tan \theta=-1\\as x is positive ,y is negative ,so \theta lies in 4th quadrant.\\tan \theta=-1=-tan 45=tan(360-45)=tan 315\\\theta=315°\\\\co-ordinates~ are~(r,theta) ~or~(-r,\theta+ -180°)\\hence ~co-ordinates~are(4√(2) ,315°),(-4√(2) ,135°)`