# Coordinate Geometry-15

### From Homeworkwiki

**Write the polar coordinates of the point (4, 4)**

**Solution:** x = r cos Θ = 4; ......................................(1)

y = r sin Θ = 4 .......................................................(ii)

Squaring and adding (i) and (ii)

r^{2} (cos^{2} Θ + sin^{2} Θ) = 4^{2} + 4^{2} = 32

i.e. r^{2} = 32 Therefore, r = √32 = √(16 x 2) = 4 √2

Dividing (ii) by (i)

tan Θ = 4/4 = 1. Therefore, Θ = 45^{0}

Hence, the polar coordinates of the point are (4√2, 45^{0})