Why is sin(30) wrong? Check degrees and radians first
The same number describes different angles in DEG and RAD. A quick reference calculation can prevent an entire worksheet of incorrect answers.
Scientific calculator →What the setting changes
A full turn is 360 degrees or 2π radians. DEG therefore reads 30 as 30°, while RAD reads it as 30 radians. The setting affects sine, cosine, tangent and their inverse functions. It does not change addition, square roots or logarithms. Choose the unit stated in your problem rather than whichever option was selected during your previous calculation.
A two-way check
In DEG, sin(30) = 0.5. In RAD, enter sin(pi/6): π/6 radians is the same angle, so the answer is again 0.5. Convert degrees to radians by multiplying by π/180; convert back by multiplying by 180/π. For inverse sine, asin(0.5) returns 30 in DEG and approximately 0.523599 in RAD.
Avoid a second common mix-up
The inverse-sine key asks which angle has a given sine. It is not the reciprocal 1/sin(x). Inverse sine accepts inputs from −1 to 1 and returns a principal angle; it does not list every angle with that sine. For triangle work, draw the diagram and check which angle is relevant before using a principal result. A tangent at 90° is undefined, not simply a very large useful measurement. A degree symbol in the source is a useful cue, but a formula may explicitly require radians.
Try the calculators
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