Determine the values of $sin(θ)$ and $cos(θ)$ for $θ = frac{5π}{6}$

Let $θ = \frac{5π}{6}$. This angle is in the second quadrant.

To find $\sin(θ)$ and $\cos(θ)$, we use the reference angle $θ’ = π – \frac{5π}{6} = \frac{π}{6}$.

The sine and cosine of $\frac{π}{6}$ are:

$\sin\left(\frac{π}{6}\right) = \frac{1}{2}, \cos\left(\frac{π}{6}\right) = \frac{\sqrt{3}}{2}$

Since the angle is in the second quadrant, $\sin(θ)$ is positive and $\cos(θ)$ is negative.

Thus,

$\sin\left(\frac{5π}{6}\right) = \frac{1}{2}, \cos\left(\frac{5π}{6}\right) = -\frac{\sqrt{3}}{2}$

The angle $θ = frac{5π}{6}$ lies in the second quadrant.

We will find the reference angle $θ’ = π – frac{5π}{6} = frac{π}{6}$.

For $frac{π}{6}$,

$sinleft(frac{π}{6}
ight) = frac{1}{2}, cosleft(frac{π}{6}
ight) = frac{sqrt{3}}{2}$

In the second quadrant, sine is positive and cosine is negative, so:

$sinleft(frac{5π}{6}
ight) = frac{1}{2}, cosleft(frac{5π}{6}
ight) = -frac{sqrt{3}}{2}$

For $θ = frac{5π}{6}$,

$sinleft(frac{5π}{6}
ight) = frac{1}{2}, cosleft(frac{5π}{6}
ight) = -frac{sqrt{3}}{2}$

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