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

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To express the angle of 12 degrees and 28 minutes in radians without using pi/180°, the conversion involves recognizing that 1 minute equals 1/60 of a degree. The calculation shows that 12° 28' can be converted to degrees as 12 + 28/60, resulting in 187/15 degrees. This value can then be expressed in radians as (187/15) * (pi/180), simplifying to 187pi/2700. An alternative method for conversion exists, but the primary approach is valid and effective.
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Express the following angle in radians.

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

I cannot apply pi/180° to this problem.
 
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You could write:

$$12^{\circ}+28'\cdot\frac{1^{\circ}}{60'}=\frac{187}{15}^{\circ}\cdot\frac{\pi}{180^{\circ}}=\frac{187\pi}{2700}$$
 
MarkFL said:
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?
 
RTCNTC said:
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.
 
There is another way to do this but it's ok.
 
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