- #1
mathdad
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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.
12 degrees, 28 minutes, that is, 12° 28'.
I cannot apply pi/180° to this problem.
MarkFL said:You could write:
\(\displaystyle 12^{\circ}+28'\cdot\frac{1^{\circ}}{60'}=\frac{187}{15}^{\circ}\cdot\frac{\pi}{180^{\circ}}=\frac{187\pi}{2700}\)
RTCNTC said:Where did (1/60°) and (187°)/15 come from?
A minute is a unit of measurement for angles, equivalent to 1/60th of a degree or 1/21600th of a full circle. In radians, a minute is approximately 0.000291 radians.
To convert minutes to degrees, simply divide the number of minutes by 60. For example, 30 minutes is equal to 30/60 = 0.5 degrees.
The formula for converting degrees to radians is: radians = (degrees * pi) / 180. This is because there are 2*pi radians in a full circle, and 180 degrees in a full circle.
There are 2*pi radians in a full circle. This is equivalent to approximately 6.283 radians.
Radians are used in advanced mathematics because they have a simpler and more elegant relationship with the properties of the circle, making calculations and formulas involving angles and circular motion easier to work with. They are also more commonly used in calculus, physics, and other scientific fields.