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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Recall the conversion formula between radians and degrees
The conversion formula is based on the relationship that $$2\pi \text{ radians} = 360°
Step 3:: Set up the proportion
\frac{\pi}{6} \text{ radians} = x°
We can set up the following proportion:
Step 4:: Use the conversion relationship
\frac{\frac{\pi}{6}}{2\pi} = \frac{x}{360}
Step 5:: Cross multiply and solve for x
\frac{\pi}{6} \cdot 360 = 2\pi \cdot x
\frac{\pi}{6} \cdot 360 = 2\pi x
Step 6:: Simplify and calculate
x = \frac{60\pi}{2\pi} = 30
60\pi = 2\pi x
Final Answer
\frac{\pi}{6} radians is equivalent to 30°.
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