Question
Convert \( 256^{\circ} \) to radians. Give your answer in exact form.
Ask by Bird Chambers. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 256^{\circ} \) in radians is \( \frac{64\pi}{45} \).
Solution
To convert degrees to radians, we use the formula:
\[
r = d \cdot \frac{\pi}{180}
\]
where \( r \) is the angle in radians and \( d \) is the angle in degrees.
For \( 256^{\circ} \), we can set up the conversion as follows:
\[
r = 256 \cdot \frac{\pi}{180}
\]
Now, let's simplify this expression.
Calculate the value by following steps:
- step0: Calculate:
\(256\times \frac{\pi }{180}\)
- step1: Reduce the numbers:
\(64\times \frac{\pi }{45}\)
- step2: Multiply:
\(\frac{64\pi }{45}\)
The exact form of \( 256^{\circ} \) converted to radians is \( \frac{64\pi}{45} \).
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Simplify this solution Mind Expander
To convert degrees to radians, you can use the conversion factor \( \frac{\pi \text{ radians}}{180^\circ} \). So, to convert \( 256^\circ \) to radians: \[ 256^\circ \times \frac{\pi \text{ radians}}{180^\circ} = \frac{256\pi}{180} \] Now we simplify \( \frac{256\pi}{180} \): \[ \frac{256\pi}{180} = \frac{128\pi}{90} = \frac{64\pi}{45} \] Thus, the exact form of \( 256^\circ \) in radians is: \[ \frac{64\pi}{45} \]
