To convert degrees to radians, we use the formula:

\[
\text{Radians} = \text{Degrees} \times \frac{\pi}{180}
\]

For 1,040°:

\[
\text{Radians} = 1,040^\circ \times \frac{\pi}{180^\circ}
\]

Simplifying the calculation:

\[
\text{Radians} = \frac{1,040\pi}{180} = \frac{52\pi}{9} \text{ radians}
\]

Thus, the radian measure of 1,040° is \(\frac{52\pi}{9}\) radians, which is approximately 18.16 radians.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you convert radians back to degrees?
2. What is the radian measure of 360°?
3. Why is \(\pi\) used in the degree-to-radian conversion?
4. What is the general formula for converting radians to degrees?
5. Can angles greater than 360° have real-world applications?

**Tip**: When converting between radians and degrees, always remember that \(180^\circ\) equals \(\pi\) radians.

Learn how to convert 1,040° to radians using the degree-to-radian conversion formula. This problem explains the step-by-step process of multiplying degrees by π/180, leading to the solution 52π/9 radians or approximately 18.16 radians. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation