Question

How can I find the angular position in radians of the minute hand of a clock at 5:00, 7:15, an 3:35?

Answer 1

A) 5:00 
At 00 minutes, the minute hand is point straight up. That is one quarter turn of the entire circle. One-fourth of 2π radians is 1/2 π, or π/2 

b) 7:15 
At 15 minutes, the minute hand is pointing straight to the right, along the imaginary positive x-axis, so it has turned through none of the circle. 0 radians.

c) 3:30 
This one isn't as clean as the others. Let's first find the 35 minute position: it occurs at hour number 7. Identify that measuring from 3 (positive x-axis, measuring counter clockwise) you have to turn through 40 minutes worth of clock. 40 minutes represents 40/60 of an entire clock, which reduces to 2/3. 2/3 of all the radians in a circle (2π of them) is 4/3π, or 4π/3. 

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