Find the coordinates of the point where the terminal side of an angle $ heta$ intersects the unit circle, given that $ heta = frac{5pi}{6}$

To determine the coordinates where the terminal side of $\theta = \frac{5\pi}{6}$ intersects the unit circle:

First, recall that on the unit circle, the coordinates are given by $(\cos(\theta), \sin(\theta))$.

Calculate the cosine and sine values:

$ \cos\left(\frac{5\pi}{6}\right) = -\frac{\sqrt{3}}{2} $

$ \sin\left(\frac{5\pi}{6}\right) = \frac{1}{2} $

Thus, the coordinates are:

$ \left( -\frac{\sqrt{3}}{2}, \frac{1}{2} \right) $

For $ heta = frac{5pi}{6}$, we use the unit circle:

Coordinates are $(cos( heta), sin( heta))$:

$ cosleft(frac{5pi}{6}
ight) = -frac{sqrt{3}}{2} $

$ sinleft(frac{5pi}{6}
ight) = frac{1}{2} $

Therefore, the coordinates are:

$ left( -frac{sqrt{3}}{2}, frac{1}{2}
ight) $

For $ heta = frac{5pi}{6}$, the coordinates are:

$ left( -frac{sqrt{3}}{2}, frac{1}{2}
ight) $

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