Math Problem Statement

Convert between degrees and radians for certain positive angles. Find the corresponding radian or degree measures.

Solution

It looks like the problem involves converting between degrees and radians. Here's the breakdown of what I see in the image:

  1. Converting 4π3\frac{4\pi}{3} radians to degrees:

    • The answer is provided as 240240^\circ.
  2. Converting 5π3\frac{5\pi}{3} radians to degrees:

    • The answer is provided as 300300^\circ.
  3. Converting 315315^\circ to radians:

    • You need to simplify this conversion.

Converting 315315^\circ to radians:

To convert degrees to radians, use the following formula:

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

For 315315^\circ:

315×π180=315π180=7π4315^\circ \times \frac{\pi}{180} = \frac{315\pi}{180} = \frac{7\pi}{4}

Thus, 315315^\circ equals 7π4\frac{7\pi}{4} radians.


Would you like further details or explanations on these conversions?

Here are 5 related questions you might consider:

  1. How do you convert any degree measure to radians?
  2. What is the significance of π\pi in the context of angle conversion?
  3. How would you convert from radians back to degrees?
  4. What are the standard angles in radians (like π2\frac{\pi}{2}, π\pi, etc.)?
  5. How do radians relate to the unit circle?

Tip: Always remember that 180=π180^\circ = \pi radians, which is key for conversions.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Radians
Degrees

Formulas

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

Theorems

Angle conversion theorem: 180 degrees equals π radians

Suitable Grade Level

Grades 9-12