Math Problem Statement

-\frac{\pi }{6} reference angle

Solution

The reference angle for π6-\frac{\pi}{6} is found by converting this angle to an equivalent positive acute angle. Here's how it's done:

  1. Since π6-\frac{\pi}{6} is negative, add 2π2\pi to find its positive coterminal angle: π6+2π=11π6-\frac{\pi}{6} + 2\pi = \frac{11\pi}{6}

  2. Determine the quadrant of 11π6\frac{11\pi}{6}:

    • 11π6\frac{11\pi}{6} is in the fourth quadrant because it's between 3π2\frac{3\pi}{2} and 2π2\pi.
  3. To find the reference angle in the fourth quadrant, subtract 11π6\frac{11\pi}{6} from 2π2\pi: 2π11π6=π62\pi - \frac{11\pi}{6} = \frac{\pi}{6}

So, the reference angle for π6-\frac{\pi}{6} is π6\frac{\pi}{6}.

Do you want details or have any questions?


  1. What are reference angles and how are they used in trigonometry?
  2. How can I determine reference angles for other negative angles?
  3. Why are reference angles always positive and acute?
  4. How do reference angles relate to trigonometric function signs in each quadrant?
  5. What is the reference angle of an angle in degrees, such as -45°?

Tip: Always add 2π2\pi to a negative angle to find a positive coterminal angle easily.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Reference Angles
Angle Measurement

Formulas

Reference angle calculation
Coterminal angles

Theorems

Quadrant determination

Suitable Grade Level

Grades 10-12