Check the picture below, those are the x,y pairs or cosine, sine values pair.
![\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse}\\\\ -------------------------------\\\\ cos\left( \frac{7\pi }{6} \right)=\cfrac{\stackrel{adjacent}{-\sqrt{3}}}{\stackrel{hypotenuse}{2}}\qquad \qquad sin\left( \frac{7\pi }{6} \right)=\cfrac{\stackrel{opposite}{1}}{\stackrel{hypotenuse}{2}}](https://tex.z-dn.net/?f=%5Cbf%20sin%28%5Ctheta%29%3D%5Ccfrac%7Bopposite%7D%7Bhypotenuse%7D%0A%5Cqquad%0Acos%28%5Ctheta%29%3D%5Ccfrac%7Badjacent%7D%7Bhypotenuse%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0Acos%5Cleft%28%20%5Cfrac%7B7%5Cpi%20%7D%7B6%7D%20%5Cright%29%3D%5Ccfrac%7B%5Cstackrel%7Badjacent%7D%7B-%5Csqrt%7B3%7D%7D%7D%7B%5Cstackrel%7Bhypotenuse%7D%7B2%7D%7D%5Cqquad%20%20%5Cqquad%20%20sin%5Cleft%28%20%5Cfrac%7B7%5Cpi%20%7D%7B6%7D%20%5Cright%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B1%7D%7D%7B%5Cstackrel%7Bhypotenuse%7D%7B2%7D%7D)
now, this is from the Unit Circle, and therefore the hypotenuse or radius wil be 1.
![\bf \begin{cases} adjacent=&-\frac{\sqrt{3}}{2}\\ opposite=&\frac{1}{2}\\ hypotenuse=&1 \end{cases}\\\\ -------------------------------\\\\ sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse} \quad % tangent tan(\theta)=\cfrac{opposite}{adjacent} \\\\\\ % cotangent cot(\theta)=\cfrac{adjacent}{opposite} \qquad % cosecant csc(\theta)=\cfrac{hypotenuse}{opposite} \quad % secant sec(\theta)=\cfrac{hypotenuse}{adjacent}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Aadjacent%3D%26-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5C%5C%0Aopposite%3D%26%5Cfrac%7B1%7D%7B2%7D%5C%5C%0Ahypotenuse%3D%261%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0Asin%28%5Ctheta%29%3D%5Ccfrac%7Bopposite%7D%7Bhypotenuse%7D%0A%5Cqquad%0Acos%28%5Ctheta%29%3D%5Ccfrac%7Badjacent%7D%7Bhypotenuse%7D%0A%5Cquad%20%0A%25%20tangent%0Atan%28%5Ctheta%29%3D%5Ccfrac%7Bopposite%7D%7Badjacent%7D%0A%5C%5C%5C%5C%5C%5C%0A%25%20cotangent%0Acot%28%5Ctheta%29%3D%5Ccfrac%7Badjacent%7D%7Bopposite%7D%0A%5Cqquad%20%0A%25%20cosecant%0Acsc%28%5Ctheta%29%3D%5Ccfrac%7Bhypotenuse%7D%7Bopposite%7D%0A%5Cquad%20%0A%25%20secant%0Asec%28%5Ctheta%29%3D%5Ccfrac%7Bhypotenuse%7D%7Badjacent%7D)
so, just plug in those values... hmmm lemme do the tangent, so you see the division of two fractions.
![\bf tan\left( \frac{7\pi }{6} \right)=\cfrac{sin\left( \frac{7\pi }{6} \right)}{cos\left( \frac{7\pi }{6} \right)}\implies tan\left( \frac{7\pi }{6} \right)=\cfrac{\frac{1}{2}}{-\frac{\sqrt{3}}{2}}\implies tan\left( \frac{7\pi }{6} \right)=\cfrac{1}{2}\cdot \cfrac{2}{-\sqrt{3}}](https://tex.z-dn.net/?f=%5Cbf%20tan%5Cleft%28%20%5Cfrac%7B7%5Cpi%20%7D%7B6%7D%20%5Cright%29%3D%5Ccfrac%7Bsin%5Cleft%28%20%5Cfrac%7B7%5Cpi%20%7D%7B6%7D%20%5Cright%29%7D%7Bcos%5Cleft%28%20%5Cfrac%7B7%5Cpi%20%7D%7B6%7D%20%5Cright%29%7D%5Cimplies%20tan%5Cleft%28%20%5Cfrac%7B7%5Cpi%20%7D%7B6%7D%20%5Cright%29%3D%5Ccfrac%7B%5Cfrac%7B1%7D%7B2%7D%7D%7B-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%7D%5Cimplies%20tan%5Cleft%28%20%5Cfrac%7B7%5Cpi%20%7D%7B6%7D%20%5Cright%29%3D%5Ccfrac%7B1%7D%7B2%7D%5Ccdot%20%5Ccfrac%7B2%7D%7B-%5Csqrt%7B3%7D%7D)
Answer:
the second one is ur answer
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The answer is A. I hope this helps, have a great day!
Answer:
9.99
Step-by-step explanation: