We must first use our knowledge of polar coordinates...
We see from this diagram, that:
#color(red)(x = rcostheta #
#color(red)(y = rsintheta #
#color(red)( r^2 = r^2cos^2x + r^2 sin^2x = x^2 + y^2 " Using pythagerous" #
#=> (x,y) -= (rcostheta , rsintheta ) #
So we can find #r#:
#r^2 = (-18)^2 + (-61)^2 #
#=> r^2 = 324 + 3721 = 4045 #
#=> r = sqrt(4045) #
We can now find #alpha#
#=> tanalpha = 61/18 #
#=> alpha = tan^(-1) (61/18) #
Now we need the angle form the positive #x# axis
So hence
#theta =alpha + pi " Radians" #
#theta = alpha + 180^circ " Degrees" #
#=> theta = tan^(-1) ( 61/18) + pi #
or #=> theta = tan^(-1) (61/18) + 180^circ #
#=> color(red)( (sqrt(4045) , tan^(-1) (61/18) + pi ) " In radians" #
#=> color(red)( (sqrt(4045) , tan^(-1) (61/18) + 180^circ) " In degrees" #
