CALCULATOR
Sine of Half a Positive Angle Calculator
Sine of Half a Positive Angle. Example: Angle: 60 degrees gives 0.5 number. Supplied angle1..179degrees; returns sine of half-angle, no sign ambiguity or unrestricted quadrant inference. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible.
Supplied angle1..179degrees; returns sine of half-angle, no sign ambiguity or unrestricted quadrant inference. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Double-angle cosine identity rearranged; θ/2 lies in first quadrant so choose positive root.
Accepted inputs: Angle: 1 to 179 degrees.
How the calculation works
sin(θ/2)=√((1-cosθ)/2)
Worked example
With angle 60 degrees, sine of half a positive angle is 0.5 number.
Assumptions and limits
Supplied angle1..179degrees; returns sine of half-angle, no sign ambiguity or unrestricted quadrant inference. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Double-angle cosine identity rearranged; θ/2 lies in first quadrant so choose positive root.