Two equations, solve for x
1°= x radians
90° = π/2 radians
1/90 = x/(π/2)
π/2 = 90x
x = π/180 ~= 0.01745 radians
Therefore: 1°= π/180 radians ~= 0.01745 radians
or easier to remember: 180° = π radians
Switching the equation around:
1 radian = (180/π)° ~= 57.2958°
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x*pi / 180 -420*3.14 / 180 = -7.33
It is an old convention where everything is perfect like a circle, and each year have 360 days (for some reason). The ancients decided to make the unit to measure angles using this system, defining the angle of a full rotation is the godly number 360, and then split down. Now, a more useful and intuitive definition is given, called a radian measure. Where the radian measure of a full rotation as the circumference of the UNIT CIRCLE (circle with radius 1), which is 2 pi.
A complete circle is 360°, which is equal to 2π radians.To convert from degrees to radians, multiply by π radians per 180°.To convert from radians to degrees, multiply by 180° per π radians.
sin(49) = - 0.9537526528 ------------------------------In radian mode. sin(49) = 0.7547095802 -----------------------------In degree mode.