Question

Picture attached 

Which set of polar coordinates are plotted in the graph below?

(-2,-4pi/3)

(2,pi/6)

(2,2pi/3)

(2,5pi/3)

Answer 1

The answer is (2,2pi/3). I just took the quiz.

Answer 2

we can see that

point is in second coordinate

so, x-value must be negative and y-value must be positive

so, we can check each options

option-A:

`(r,\theta)=(-2,-(4\pi)/(3) )`

`x=rcos(\theta)`

`x=-2cos(-(4\pi)/(3) )`

`x=1`

since, x-value is positive

so, this is FALSE

option-B:

`(r,\theta)=(2,(\pi)/(6) )`

`x=rcos(\theta)`

`x=2cos((\pi)/(6))`

`x=√(3)`

`y=rsin(\theta)`

`y=2sin((\pi)/(6))`

`y=1`

since, y-value is positive

so, this is FALSE

option-C:

`(r,\theta)=(2,(2\pi)/(3) )`

`x=rcos(\theta)`

`x=2cos((2\pi)/(3))`

`x=-1`

`y=rsin(\theta)`

`y=2sin((2\pi)/(3))`

`y=√(3)`

Since, x-value is negative and y-value is positive

so, this is TRUE

option-D:

`(r,\theta)=(2,(5\pi)/(3) )`

`x=rcos(\theta)`

`x=2cos((5\pi)/(3))`

`x=1`

Since, x-value is positive

so, this is FALSE