Advanced Functions Trigonometry

Question

1. Though how many radians does the second hand of a clock move in 2 minutes and 40 seconds.

 

This question is one of the units in Advanced Functions, I really have hard time answering this question. 

Answer 1

The second hand makes 1 rotation for 1 min. 1 rotation equals 2π radians.

The second hand makes 2 rotations for 2 min, that is 4π

40 sec = 40 sec • (1 min/60 sec) = 2/3 min.

For 40 sec, the second hand makes 2/3 of a rotation, which as an angle is 2/3 • 2π =4/3 π radians.

 

We add the rotations for 2 min and 40 sec and get

4π + 4/3 π = 5 1/3 π radians.

It is approximately

16.7 radians