$ ext{Find the sine, cosine, and tangent values of the given angles on the unit circle}$

$ \text{Consider the angle } \theta = \frac{7\pi}{6} $

$ \text{Step 1: Find the sine value } \sin\left(\frac{7\pi}{6}\right) = -\frac{1}{2} $

$ \text{Step 2: Find the cosine value } \cos\left(\frac{7\pi}{6}\right) = -\frac{\sqrt{3}}{2} $

$ \text{Step 3: Calculate tangent } \tan\left(\frac{7\pi}{6}\right) = \frac{\sin\left(\frac{7\pi}{6}\right)}{\cos\left(\frac{7\pi}{6}\right)} = \frac{-\frac{1}{2}}{-\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3} $

$ \text{Answer: } \sin\left(\frac{7\pi}{6}\right) = -\frac{1}{2}, \cos\left(\frac{7\pi}{6}\right) = -\frac{\sqrt{3}}{2}, \tan\left(\frac{7\pi}{6}\right) = \frac{\sqrt{3}}{3} $

$ ext{Consider the angle } heta = frac{5pi}{4} $

$ ext{Step 1: Find the sine value } sinleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

$ ext{Step 2: Find the cosine value } cosleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

$ ext{Step 3: Calculate tangent } anleft(frac{5pi}{4}
ight) = frac{sinleft(frac{5pi}{4}
ight)}{cosleft(frac{5pi}{4}
ight)} = frac{-frac{sqrt{2}}{2}}{-frac{sqrt{2}}{2}} = 1 $

$ ext{Answer: } sinleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2}, cosleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2}, anleft(frac{5pi}{4}
ight) = 1 $

$ heta = frac{4pi}{3} $

$ sinleft(frac{4pi}{3}
ight) = -frac{sqrt{3}}{2}, cosleft(frac{4pi}{3}
ight) = -frac{1}{2}, anleft(frac{4pi}{3}
ight) = sqrt{3} $

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