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:
[tex] (r,\theta)=(-2,-\frac{4\pi}{3} ) [/tex]
[tex] x=rcos(\theta) [/tex]
[tex] x=-2cos(-\frac{4\pi}{3} ) [/tex]
[tex] x=1 [/tex]
since, x-value is positive
so, this is FALSE
option-B:
[tex] (r,\theta)=(2,\frac{\pi}{6} ) [/tex]
[tex] x=rcos(\theta) [/tex]
[tex] x=2cos(\frac{\pi}{6}) [/tex]
[tex] x=\sqrt{3} [/tex]
[tex] y=rsin(\theta) [/tex]
[tex] y=2sin(\frac{\pi}{6}) [/tex]
[tex] y=1 [/tex]
since, y-value is positive
so, this is FALSE
option-C:
[tex] (r,\theta)=(2,\frac{2\pi}{3} ) [/tex]
[tex] x=rcos(\theta) [/tex]
[tex] x=2cos(\frac{2\pi}{3}) [/tex]
[tex] x=-1 [/tex]
[tex] y=rsin(\theta) [/tex]
[tex] y=2sin(\frac{2\pi}{3}) [/tex]
[tex] y=\sqrt{3} [/tex]
Since, x-value is negative and y-value is positive
so, this is TRUE
option-D:
[tex] (r,\theta)=(2,\frac{5\pi}{3} ) [/tex]
[tex] x=rcos(\theta) [/tex]
[tex] x=2cos(\frac{5\pi}{3}) [/tex]
[tex] x=1 [/tex]
Since, x-value is positive
so, this is FALSE
