Question

question given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function. \\(\sin 330^{\circ}\\) show examples

Explanation:

Step1: Determine the reference angle

The angle $330^\circ$ is in the fourth quadrant. To find the reference angle, we use the formula: for an angle $\theta$ in the fourth quadrant, the reference angle $\alpha = 360^\circ - \theta$. So, $\alpha = 360^\circ - 330^\circ = 30^\circ$.

Step2: Recall the sine value of the reference angle

We know that $\sin 30^\circ=\frac{1}{2}$.

Step3: Determine the sign of the sine function in the fourth quadrant

In the fourth quadrant, the sine function (which represents the y - coordinate on the unit circle) is negative. So, $\sin 330^\circ=-\sin 30^\circ$.

Step4: Calculate the value of $\sin 330^\circ$

Substituting the value of $\sin 30^\circ$ into the equation, we get $\sin 330^\circ =-\frac{1}{2}$.

Answer:

$-\frac{1}{2}$