Math Problem Statement

What is the reference angle for 150 degrees

Solution

The reference angle is the acute angle formed between the terminal side of a given angle and the x-axis. For an angle in standard position, the reference angle is always positive and less than or equal to 90°.

For 150°, which lies in the second quadrant, the reference angle is calculated by subtracting the angle from 180°:

Reference angle=180150=30\text{Reference angle} = 180^\circ - 150^\circ = 30^\circ

So, the reference angle for 150° is 30 degrees.

Would you like further details on this? Here are some related questions:

  1. What is the reference angle for 210 degrees?
  2. How do you find the reference angle for an angle in radians?
  3. What is the reference angle for negative angles, like -120 degrees?
  4. How does the quadrant affect the calculation of the reference angle?
  5. What is the reference angle for 315 degrees?

Tip: The reference angle is always measured from the terminal side of the angle to the x-axis, regardless of the quadrant.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Reference Angles
Angles in Quadrants

Formulas

Reference angle = 180° - given angle (for angles in the second quadrant)

Theorems

Reference Angle Theorem

Suitable Grade Level

Grades 9-12