# What are the polar coordinates of #(18, −6)#?

##### 1 Answer

Jan 23, 2016

#( 6sqrt10 , - 0.32 ) #

#### Explanation:

Using the formulae that links Cartesian to Polar coordinates .

#• r^2 = x^2 + y^2 #

#• theta = tan^-1 (y/x ) # [ The point (18 , -6 ) is in the 4th quadrant and care must be

taken to ensure

# theta# is in the 4th quadrant. ](here x = 18 and y = - 6 )

# r^2 = 18^2 + (-6)^2 = 324 + 36 = 360 #

#rArr r = sqrt360 = 6sqrt10 # and

# theta =tan^-1 (-6/10) = - 0.32 color(black)(" radians ")# This is an angle in the 4th quadrant.