How can you express an angle in radians without using pi/180°?

[mathdad]

Express the following angle in radians.

12 degrees, 28 minutes, that is, 12° 28'.

I cannot apply pi/180° to this problem.

 

[MarkFL]

You could write:

$$12^{\circ}+28'\cdot\frac{1^{\circ}}{60'}=\frac{187}{15}^{\circ}\cdot\frac{\pi}{180^{\circ}}=\frac{187\pi}{2700}$$

 

[mathdad]

You could write:

$$12^{\circ}+28'\cdot\frac{1^{\circ}}{60'}=\frac{187}{15}^{\circ}\cdot\frac{\pi}{180^{\circ}}=\frac{187\pi}{2700}$$

Where did (1/60°) and (187°)/15 come from?

 

[MarkFL]

Where did (1/60°) and (187°)/15 come from?

$$\frac{1^{\circ}}{60'}$$ is a fraction equal to 1 used to convert from minutes to degrees. And then:

$$12+\frac{28}{60}=\frac{187}{15}$$

And this is in degrees.

 

[mathdad]

There is another way to do this but it's ok.