Math Problem Statement

Express: i. 22° in radians. ii. π/10 radians in degrees.

Solution

The image presents Question 5, which contains two parts:

  1. Convert 22° to radians.
  2. Convert π10\frac{\pi}{10} radians to degrees.

Let's solve each part:

i. Convert 2222^\circ to radians:

The formula to convert degrees to radians is: Radians=Degrees×π180\text{Radians} = \text{Degrees} \times \frac{\pi}{180} Substitute 2222^\circ into the formula: 22×π180=22π180=11π9022^\circ \times \frac{\pi}{180} = \frac{22\pi}{180} = \frac{11\pi}{90} So, 2222^\circ is 11π90\frac{11\pi}{90} radians.

ii. Convert π10\frac{\pi}{10} radians to degrees:

The formula to convert radians to degrees is: Degrees=Radians×180π\text{Degrees} = \text{Radians} \times \frac{180}{\pi} Substitute π10\frac{\pi}{10} into the formula: π10×180π=18010=18\frac{\pi}{10} \times \frac{180}{\pi} = \frac{180}{10} = 18^\circ So, π10\frac{\pi}{10} radians is 1818^\circ.

Final Answers:

  1. 22=11π9022^\circ = \frac{11\pi}{90} radians.
  2. π10\frac{\pi}{10} radians = 1818^\circ.

Would you like more details or have any questions?

Here are five related questions for practice:

  1. Convert 4545^\circ to radians.
  2. What is 11 radian in degrees?
  3. Convert π6\frac{\pi}{6} radians to degrees.
  4. Convert 120120^\circ to radians.
  5. How many radians are in a full circle (360°)?

Tip: Always remember that π\pi radians = 180°, which can help in quick conversions between degrees and radians.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Unit Conversion

Formulas

Radians = Degrees × (π / 180)
Degrees = Radians × (180 / π)

Theorems

Radians and Degrees Conversion

Suitable Grade Level

Grades 9-11