We must first use our knowledge of polar coordinates...
![enter image source here]()
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)
![enter image source here]()
We can now find alpha
=> tanalpha = 61/18
=> alpha = tan^(-1) (61/18)
Now we need the angle form the positive x axis
![enter image source here]()
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"
