Name the reference angle for $$ -120^{\circ} $$. $$ \hat{ heta}=\square^{\circ} $$

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Name the reference angle for $$ -120^{\circ} $$. $$ \hat{	heta}=\square^{\circ} $$

UpStudy AI · Accepted Answer

To find the reference angle for $$ -120^{\circ} $$, follow these steps:

1. **Convert to Positive Angle:**
   Since the angle is negative, add $$ 360^{\circ} $$ to find its positive equivalent:
   $$
   -120^{\circ} + 360^{\circ} = 240^{\circ}
   $$
   
2. **Determine the Quadrant:**
   $$ 240^{\circ} $$ lies in the **third quadrant** (between $$ 180^{\circ} $$ and $$ 270^{\circ} $$).

3. **Calculate the Reference Angle:**
   The reference angle ($$ \hat{\theta} $$) is the acute angle formed by the terminal side of $$ 240^{\circ} $$ and the x-axis:
   $$
   \hat{\theta} = 240^{\circ} - 180^{\circ} = 60^{\circ}
   $$

**Final Answer:**
$$
\hat{\theta} = 60^{\circ}
$$
The reference angle for $$ -120^{\circ} $$ is $$ 60^{\circ} $$.

Name the reference angle for \( -120^{\circ} \). \( \hat{\theta}=\square^{\circ} \)

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