Answer the following. Round your answers to the nearest hundredth.

(a) Convert [tex]$\frac{2 \pi}{11}$[/tex] radians to degree measure.
[ ] °
(b) Convert [tex]$288^{\circ}$[/tex] to radian measure.
[ ] radians

To convert radians to degrees, multiply by π 180 ​ . 11 2 π ​ × π 180 ​ ≈ 32.7 3 ∘ .
To convert degrees to radians, multiply by 180 π ​ . 28 8 ∘ × 180 π ​ ≈ 5.03 radians.
The radian measure of 28 8 ∘ is approximately 5.03 radians.
The degree measure of 11 2 π ​ radians is approximately 32.7 3 ∘ ​ and the radian measure of 28 8 ∘ is approximately 5.03 radians ​ .

Explanation

Problem Analysis Let's convert radians to degrees and degrees to radians.

Convert radians to degrees (a) To convert radians to degrees, we multiply the radian measure by π 180 ​ . So, we have: 11 2 π ​ ⋅ π 180 ​ = 11 2 ⋅ 180 ​ = 11 360 ​ ≈ 32.7 3 ∘ Therefore, 11 2 π ​ radians is approximately 32.7 3 ∘ .

Convert degrees to radians (b) To convert degrees to radians, we multiply the degree measure by 180 π ​ . So, we have: 28 8 ∘ ⋅ 180 π ​ = 180 288 π ​ = 5 8 π ​ ≈ 5.03 radians Therefore, 28 8 ∘ is approximately 5.03 radians.

Final Answer The answers are: (a) 32.7 3 ∘ (b) 5.03 radians


Examples
Understanding radian and degree conversions is crucial in fields like astronomy, where angles in the sky are measured, and in engineering, for designing circular structures or calculating rotational motion. For instance, an astronomer might need to convert the angular size of a star (measured in radians) to degrees for easier communication with the public, or an engineer might convert the degree measure of a gear's rotation to radians for precise calculations in a mechanical system.

Answered by GinnyAnswer | 2025-07-05

To convert 11 2 π ​ radians to degrees, the result is approximately 32.7 3 ∘ . To convert 28 8 ∘ to radians, the result is approximately 5.03 radians.
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Answered by Anonymous | 2025-07-17