Minutes, Degrees, Seconds to Radians

[mathdad]

Express the following angle in radians.

12 degrees, 28 minutes, 4 seconds that is, 12° 28' 4".

I cannot apply pi/180° to this problem.

 

[MarkFL]

Use the same method I posted in your other thread, and use the fact that there are 3600 seconds in a degree. :D

 

[HallsofIvy]

Why can't you "apply pi/180" here?

You know that there are 60 seconds in a degree don't you? So 4''= 4/60= 0.06667 minutes approximately and 28' 4'' is 28.06667 minutes. And you know, I hope, that there are 60 minutes in a degree so that 28.06667 minutes is 28.06667/60= 0.4678 degrees. 12 degrees, 28 minutes, 4 seconds is 12.4678 degrees. Multiply that by pi/180.

 

[mathdad]

Use the same method I posted in your other thread, and use the fact that there are 3600 seconds in a degree. :D

Is there another way to solve this problem?

 

[MarkFL]

Is there another way to solve this problem?

What you want to do is convert strictly to degrees, and then to radians.

\(\displaystyle 12^{\circ}28'4''=\left(12+\frac{28}{60}+\frac{4}{3600}\right)^{\circ}\cdot\frac{\pi}{180^{\circ}}=\frac{11221\pi}{162000}\)

 

[mathdad]

It's all coming back to me now.