Question

BRAINLIEST ASAP! PLEASE HELP ME :)

Answer 1

Answer:

○$\displaystyle -\frac{2\sqrt{3}}{3}\:[or\:-\frac{2}{\sqrt{3}}]$

Step-by-step explanation:

You have to know the Unit Circle on this one. So, to start off, in the degree-angle range from 180° - 270° [Quadrant III], you must figure out the cosine value that gives you −½, and according to the graph, theta will be represented as 240°. So, now that we have our θ, looking at the y-value 240°, since we want the cosecant function, all we have to do is take the multiplicative inverse of $\displaystyle -\frac{\sqrt{3}}{2},$which gives you $\displaystyle -\frac{2\sqrt{3}}{3}.$

Extended Information

$\displaystyle y-coordinate → sin\:θ \\ x-coordinate → cos\:θ$

$\displaystyle -\frac{2\sqrt{3}}{3} = [-\frac{\sqrt{3}}{2}]^{-1}$

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