Question

the graph below shows the angle a = 330° inside the unit circle. what is the reference angle? degrees the graph below shows the angle a = 300° inside the unit circle. what is the reference angle? degrees

Explanation:

Step1: Determine the quadrant of \(330^{\circ}\)

Since \(270^{\circ}<330^{\circ}<360^{\circ}\), \(330^{\circ}\) is in the fourth quadrant.

Step2: Calculate the reference angle for \(330^{\circ}\)

The formula for the reference angle \(\theta_{r}\) of an angle \(\theta\) in the fourth quadrant is \(\theta_{r}=360^{\circ}-\theta\).
So, \(\theta_{r}=360^{\circ} - 330^{\circ}=30^{\circ}\)

Step3: Determine the quadrant of \(300^{\circ}\)

Since \(270^{\circ}<300^{\circ}<360^{\circ}\), \(300^{\circ}\) is in the fourth quadrant.

Step4: Calculate the reference angle for \(300^{\circ}\)

Using the formula \(\theta_{r}=360^{\circ}-\theta\) (for fourth - quadrant angles), we have \(\theta_{r}=360^{\circ}-300^{\circ} = 60^{\circ}\)

Answer:

For \(A = 330^{\circ}\), the reference angle is \(30\) degrees.
For \(A = 300^{\circ}\), the reference angle is \(60\) degrees.