Question
Convert the angle \( \theta=35^{\circ} \) to radians. Express your answer exactly.
Ask by Harper Macdonald. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\theta = \frac{7\pi}{36} \text{ radians}
\]
Solution
To convert an angle from degrees to radians, you can use the conversion factor \(\frac{\pi}{180}\), since \(180^\circ = \pi\) radians.
Given:
\[
\theta = 35^\circ
\]
Convert to radians:
\[
\theta \text{ (in radians)} = 35^\circ \times \frac{\pi}{180} = \frac{35\pi}{180}
\]
Simplify the fraction by dividing the numerator and denominator by 5:
\[
\frac{35\pi}{180} = \frac{7\pi}{36}
\]
**Final Answer:**
\[
\theta = \frac{7\,\pi}{36} \text{ radians}
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To convert degrees to radians, you can use the conversion factor \( \frac{\pi \text{ radians}}{180^{\circ}} \). So, to convert \( 35^{\circ} \) to radians, you multiply: \[ \theta = 35^{\circ} \times \frac{\pi \text{ radians}}{180^{\circ}} = \frac{35\pi}{180} = \frac{7\pi}{36} \] Thus, \( \theta \) in radians is exactly \( \frac{7\pi}{36} \).
