Math Problem Statement

Convert the angle in radians to degrees.

StartFraction 5 pi Over 18 EndFraction

Solution

To convert an angle from radians to degrees, you can use the conversion factor:

degrees=radians×180π\text{degrees} = \text{radians} \times \frac{180}{\pi}

For the angle 5π18\frac{5\pi}{18} radians, the conversion to degrees is:

5π18×180π\frac{5\pi}{18} \times \frac{180}{\pi}

The π\pi cancels out:

5×18018=90018=50\frac{5 \times 180}{18} = \frac{900}{18} = 50^\circ

So, 5π18\frac{5\pi}{18} radians is equal to 5050^\circ.

Would you like more details on this conversion or have any other questions?


Here are some related questions you might be interested in:

  1. How do you convert degrees to radians?
  2. What is the degree measure of 2π3\frac{2\pi}{3} radians?
  3. How do you simplify expressions involving radians and degrees?
  4. What is the radian measure of 9090^\circ?
  5. How do you express π4\frac{\pi}{4} radians in degrees?
  6. What is the degree measure of 11 radian?
  7. How do you handle conversions when the angle is negative?
  8. What is the degree measure of 7π6\frac{7\pi}{6} radians?

Tip: When converting from radians to degrees, the key factor is 180π\frac{180}{\pi}. Multiplying by this will give you the angle in degrees.

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Math Problem Analysis

Mathematical Concepts

Trigonometry

Formulas

Radians to degrees conversion formula: degrees = radians * 180 / π

Theorems

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Suitable Grade Level

High School