Calculate the exact value of $sin(frac{5π}{6})$ and verify it on the unit circle.

To find the exact value of $\sin(\frac{5π}{6})$, we first determine the corresponding angle in degrees. Converting radians to degrees:

$\frac{5π}{6} \times \frac{180^\circ}{π} = 150^\circ$

Now, considering the unit circle, the angle $150^\circ$ lies in the second quadrant where the sine value is positive. The reference angle for $150^\circ$ is:

$180^\circ – 150^\circ = 30^\circ$

We know from the unit circle that:

$\sin(30^\circ) = \frac{1}{2}$

Therefore,

$\sin(150^\circ) = \sin(\frac{5π}{6}) = \frac{1}{2}$

To evaluate $sin(frac{5π}{6})$, we convert the angle to degrees:

$frac{5π}{6} imes frac{180^circ}{π} = 150^circ$

The unit circle tells us the sine value for angles. The reference angle for $150^circ$ is:

$180^circ – 150^circ = 30^circ$

In the second quadrant, sine values are positive. Specifically:

$sin(30^circ) = frac{1}{2}$

Thus:

$sin(150^circ) = sin(frac{5π}{6}) = frac{1}{2}$

First, convert $frac{5π}{6}$ to degrees:

$frac{5π}{6} imes 180^circ / π = 150^circ$

Since $150^circ$ is in the second quadrant where sine is positive, and its reference angle is $30^circ$:

$sin(30^circ) = frac{1}{2}$

Therefore,

$sin(150^circ) = sin(frac{5π}{6}) = frac{1}{2}$

Start Using PopAi Today