Convert 6 radians into degree measure.
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Step-by-Step Solution
Step 1: Recall the conversion formula
To convert radians to degrees, we use the fundamental relationship between radians and degrees. We know that π radians is equivalent to 180 degrees.
Step 2: Derive the conversion factor
From the relationship π radians=180∘, we can find the value of 1 radian in degrees by dividing both sides by π. This gives us the conversion factor.
Step 3: Apply the conversion factor
Now, to convert 6 radians to degrees, we multiply 6 by the conversion factor we just derived, which is π180.
Step 4: Calculate the value
Substitute the approximate value of π≈3.14159 into the expression and perform the multiplication to get the degree measure. The result is approximately 343.77 degrees.