Convert 40∘20′ into radian measure.
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Step-by-Step Solution
Step 1: Convert minutes to degrees
First, we need to convert the given angle from degrees and minutes into a single decimal degree value. Since there are 60 minutes in 1 degree, we divide the minutes by 60 to convert them into degrees.
Step 2: Express the angle in decimal degrees
Now, we add the converted minutes (in degrees) to the whole degree part of the angle. This gives us the total angle expressed entirely in degrees as a single fraction.
Step 3: Convert degrees to radians
To convert degrees to radians, we use the conversion factor that 1 degree is equal to 180π radians. This is derived from the fact that 180∘=π radians.
Step 4: Calculate the radian measure
Finally, we multiply the angle in degrees by the conversion factor 180π to get the equivalent angle in radians. We simplify the resulting fraction.