How to convert from rectangilar to polar.1.(-2,2) 2.(-4v3,4).And polar to rectangular (-5,pi/6).Please show step it would really help me

Question

How to convert from rectangilar to polar.1.(-2,2) 2.(-4√3,4).And polar to rectangular (-5,pi/6).Please show step it would really help me

Answer 1

There are two equations you need to know for converting from rectangular to polar. They are:

r^2 = x^2 + y^2

theta = invtan(y/x)

 

  ***invtan stands for inverse tangent

 

So for problem 1, your point is (-2,2):

 

r^2 = x^2 + y^2

r^2 = (-2)^2 + (2)^2

r^2 = 4 + 4

r^2 = 8

r = sqrt(8)

 

theta = invtan(2/-2)

theta = invtan(-1)

theta = 7pi/4  (remember, x is positive and y is negative putting it in the 4th quadrant)

 

So your point converts to (sqrt(8), 7pi/4)

 

For problem 2, your point is (-4sqrt(3),4):

 

r^2 = x^2 + y^2

r^2 = (4sqrt(3))^2 + (4)^2

r^2 = 48 + 16

r^2 = 64

r = 8

 

theta = invtan(4/-4sqrt(3))

theta = invtan(-1/sqrt(3))

theta = 5pi/6 (since x is negative and y is positive, the point is in the second quadrant)

 

So your point converts to (8, 5pi/6)

 

When converting from polar to rectangular, you need to remember these two equations:

x = r*cos(theta)

y = r*sin(theta)

 

For problem 3, your point is (-5, pi/6)

x = r*cos(theta)

x = -5*cos(pi/6)

x = -5(sqrt(3)/2)

 

y= r*sin(theta)

y = -5*sin(pi/6)

y = -5(1/2)

 

So your point converts to (-5sqrt(3)/2, -5/2)