Radians and degrees are two different systems for measuring the size of an angle. In radians, a full circle is 2pi radians. In degrees, a full circle is 360 degrees.
If you want to evaluate an expression in both, then first simplify and evaluate the expression plugging in radian values into your trig functions. The second time, use degree values. On your calculator, you can switch modes between radians and degrees. It should give you the same answer unless you are supposed to leave it written as unevaluated trig functions or something like that.
To convert from radians to degrees...
radians=degrees * (pi/180)
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If you are asking for the conversion formulas, then think of the relationship between degress and radians. 360 degress = 2*pi radians, thus to convert every degree to radians, we divide both sides of the equation by 360. 1 degree = 2*pi/360 radians = pi/180 radians. thus to convert degrees into radians, just multiply the number of degrees to pi/180, where pi = 3.141592... by the way, the per sec appended on the unit does not matter in the conversion since both units are in per sec anyway
kind of hard to explain over the internet but I'll try my best. one circle (ie one full clock, one full 60 minutes) is 360 degrees, or 2pi radians, so 42/60 = x/360 or x/2pi if you want it in radians. multiply both sides by 360, or 2pi, again if you want it in radians. the answer is 252 degrees or 1.4pi radians. 42/60 = x/360 (42X360)/60 = x x= 252
To find the angle whose sine is 0.151, you can use the inverse sine function (arcsin). Using a calculator, the angle is approximately 8.68 degrees or 0.151 radians. Keep in mind that sine is positive in both the first and second quadrants, so the angle could also be 171.32 degrees (or 3.00 radians) if considering the range of possible angles.
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You can:* Add the same expression to both sides of an equation * Subtract the same expression from both sides * Multiply the same expression (must not be zero) to both sides * Divide both sides by the same expression (must not be zero)