Math Problem Statement

Certain positive angles are marked in the given figure. Find the corresponding radian or degree measures.

Solution

From the image, it looks like you're working on converting angles between radians and degrees.

Let's break down each part of the problem:

  1. Given conversion for 60°:

    • 60=π360^\circ = \frac{\pi}{3} radians.
    • This is a known conversion. The relationship between degrees and radians is: radians=degrees×π180\text{radians} = \text{degrees} \times \frac{\pi}{180}
  2. Next step, converting 2π3\frac{2\pi}{3} radians to degrees:

    • To convert radians to degrees, use: degrees=radians×180π\text{degrees} = \text{radians} \times \frac{180}{\pi} 2π3×180π=120\frac{2\pi}{3} \times \frac{180}{\pi} = 120^\circ So, 2π3\frac{2\pi}{3} radians equals 120120^\circ, which matches the provided answer.
  3. Final question, converting 3π4\frac{3\pi}{4} radians to degrees:

    • Applying the same formula: 3π4×180π=135\frac{3\pi}{4} \times \frac{180}{\pi} = 135^\circ So, 3π4\frac{3\pi}{4} radians equals 135135^\circ.

Would you like more details or have any other questions?

Here are five related questions to consider:

  1. How do you convert degrees to radians?
  2. What is the general formula for converting between degrees and radians?
  3. Can you convert 9090^\circ to radians?
  4. What is the radian measure of a full circle (360°)?
  5. How would you convert π2\frac{\pi}{2} radians into degrees?

Tip: Always remember the conversion factor π radians=180\pi \text{ radians} = 180^\circ to switch between degrees and radians.

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Math Problem Analysis

Mathematical Concepts

Angle Conversion
Radians
Degrees

Formulas

radians = degrees × (π / 180)
degrees = radians × (180 / π)

Theorems

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Suitable Grade Level

Grades 9-12