Math Problem Statement

Note: Give exact answers using fractions and/or multiples of pi as necessary.

a. Convert the following angles from degrees to radians. a1. 36o = ​   radians a2. 60o = ​   radians a3. 90o = ​   radiansb. Write a general formula for converting an angle of x degrees into radians. Note: Do not include units in your formula. x degrees = ​   radians

Solution

a. Convert the following angles from degrees to radians

The formula to convert degrees to radians is:
radians=degrees×π180\text{radians} = \text{degrees} \times \frac{\pi}{180}

a1. 3636^\circ:

36×π180=36180π=π536 \times \frac{\pi}{180} = \frac{36}{180} \pi = \frac{\pi}{5} Answer: π5\frac{\pi}{5} radians

a2. 6060^\circ:

60×π180=60180π=π360 \times \frac{\pi}{180} = \frac{60}{180} \pi = \frac{\pi}{3} Answer: π3\frac{\pi}{3} radians

a3. 9090^\circ:

90×π180=90180π=π290 \times \frac{\pi}{180} = \frac{90}{180} \pi = \frac{\pi}{2} Answer: π2\frac{\pi}{2} radians


b. General formula for converting xx degrees into radians:

x degrees=x×π180 radiansx \text{ degrees} = x \times \frac{\pi}{180} \text{ radians}


Let me know if you'd like further clarifications or details.
Here are some related questions for you to explore:

  1. Why is the factor π180\frac{\pi}{180} used for converting degrees to radians?
  2. How would you convert radians back to degrees?
  3. What is the radian equivalent of 180180^\circ?
  4. What are the advantages of using radians over degrees in trigonometry?
  5. Can you derive the formula for arc length using radians?

Tip: Always remember that π\pi radians equals 180180^\circ, which forms the basis for all degree-radian conversions!

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Math Problem Analysis

Mathematical Concepts

Angle Conversion
Radians
Degrees

Formulas

radians = degrees × (π / 180)

Theorems

Definition of Radian

Suitable Grade Level

Grades 9-10