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4. Convert \( 135^{\circ} \) to radians.

Ask by Hodgson Davey. in the United States
Mar 21,2025

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Answer

\( 135^\circ \) is equal to \( \frac{3\pi}{4} \) radians.

Solution

1. Use the conversion formula from degrees to radians: \[ \text{Radians} = \text{Degrees} \times \frac{\pi}{180} \] 2. Substitute \( 135^{\circ} \) into the formula: \[ 135^\circ \times \frac{\pi}{180} \] 3. Simplify the fraction: \[ \frac{135}{180} = \frac{3}{4} \] 4. Write the final result in radians: \[ \frac{3\pi}{4} \]

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To convert degrees to radians, you use the formula: \( \text{radians} = \frac{\pi}{180} \times \text{degrees} \). So, for \( 135^{\circ} \): \[ 135^{\circ} \times \frac{\pi}{180} = \frac{135\pi}{180} = \frac{3\pi}{4} \] Thus, \( 135^{\circ} \) is equal to \( \frac{3\pi}{4} \) radians. Want to impress your friends with your math skills? Try converting other angles too, like \( 45^{\circ} \) or \( 270^{\circ} \)! It’s a fun way to get familiar with radian measures, plus you can use it in everyday situations, like finding the angle for slices of pizza or the wedge of a pie. Also, don't forget that knowing how to convert between degrees and radians is especially useful in trigonometry! Many mathematical formulas and functions are based on radians, so get comfortable with them, and you’ll be a math whiz in no time!

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