Give three different polar points that are at the same position as A = (-2, 11𝝅/6)

Question

Give three different polar points that are at the same position as A = (-2, 11𝝅/6)

You can use degrees or radians in the angle, but remember to use the degree symbol if you give an angle in degrees.

Point 1=?

Point 2=?

Point 3=?

I'm a little confused. Anybody know how I should proceed? Please explain how you found the answer.

Answer 1

given point (-2, 11pi/6)

1st point (2, 5pi/6)= (2, 11pi/6 -pi)=(2,11pi/6-6pi/6)=(2,(11-6)pi/6)

2nd point (2, -7pi/6)= (2, 11pi/6-pi)=(2, 11pi/6-6pi/6)=(2,(11-6)pi/6)

3rd point (-2, -pi/6) =(-2, 11pi/6-2pi)=(-2,11pi/6-12pi/6)=(-2,(11-12)pi/6)

keep r, the magnitude, the same, then add nor subtract 2pi=12pi/6=360 degrees to the angle

or change the sign of r, the magnitude, & add or subtract pi=6pi/6 = 180 degrees to the angle

it helps to graph "them,"or it. they're all the same point.

and maybe

convert to the rectangular coordinates

(x,y)=(rcosT, rsinT)=(2cos150, 2sin150)=(-sqr3, 1)

=(r, Theta)=sqr(x^2+y^2, tan^-1(y/x))=(sqr(3+1), tan^-1(1/-sqr3))=(2, 150 degrees)

or do the degrees equivalent too

(2, 150 degrees)=(-2,-30 degrees)=(-2,330, degrees)=(2,-210 degrees)

that you're likely more familiar or more comfortable with

Answer 2

See the video.

You can use this calculator to plot polar coordinates: https://www.geogebra.org/m/DRTYZZC6