What is the reference angle of 240°?
Understand the Problem
The question is asking for the reference angle of 240 degrees, which involves determining the smallest positive acute angle between the terminal side of 240 degrees and the x-axis.
Answer
The reference angle of $240^\circ$ is $60^\circ$.
Answer for screen readers
The reference angle of $240^\circ$ is $60^\circ$.
Steps to Solve
-
Identify the quadrant of the angle The angle of $240^\circ$ is located in the third quadrant because it is between $180^\circ$ and $270^\circ$.
-
Determine the reference angle formula for the third quadrant For angles in the third quadrant, the reference angle can be found using the formula: $$ \text{Reference angle} = \theta - 180^\circ $$
-
Calculate the reference angle Substituting $\theta$ with $240^\circ$: $$ \text{Reference angle} = 240^\circ - 180^\circ = 60^\circ $$
-
Confirm the result The reference angle is the smallest positive acute angle between the terminal side of $240^\circ$ and the x-axis, which we calculated to be $60^\circ$.
The reference angle of $240^\circ$ is $60^\circ$.
More Information
The reference angle is a crucial concept in trigonometry, often used in solving problems involving triangles and circles. It helps in applying trigonometric functions correctly within different quadrants.
Tips
- Confusing the reference angle formula: Some may mistakenly subtract $240^\circ$ from $360^\circ$, which is incorrect for an angle in the third quadrant.
- Not recognizing the quadrant: It's essential to determine which quadrant the angle is in to apply the correct formula.
AI-generated content may contain errors. Please verify critical information
