keeping in mind that, if we convert the "improper" π fraction to a mixed π fraction, we'd get
[tex]\bf \cfrac{7}{3}\implies \cfrac{3+3+1}{3}\implies \cfrac{3}{3}+\cfrac{3}{3}+\cfrac{11}{3}\implies 1+1+\cfrac{1}{3}\implies 2+\cfrac{1}{3}
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\textit{or just }2\frac{1}{3}\qquad therefore\qquad -\cfrac{7\pi }{3}\implies -2\pi -\cfrac{1\pi }{3}\implies -2\pi -\cfrac{\pi }{3}[/tex]
now, check the picture below, the angle is just a full revolution, "clockwise", and then π/3 extra, that's the angel on the IV quadrant.
using the period I assume it means the cycle, and you can just check your Unit Circle to see what the sine of that angle is.
