What is the half-angle formula? Half-angle formula is a formula for finding trigonometric functions such as sine, cosine and tangent of an angle (such as ∠A).
The half-angle formula commonly used in junior high school mathematics is summarized as sin (a/2) = √ ((1-COSA)/2); sin(A/2)=-√(( 1-cosA)/2)
cos(A/2)=√(( 1+cosA)/2); cos(A/2)=-√(( 1+cosA)/2)
tan(A/2)=√(( 1-cosA)/(( 1+cosA)); tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
ctg(A/2)=√(( 1+cosA)/(( 1-cosA)); ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
The derivation process of the half-angle formula is based on the double-angle formula: CO2A = 1-2 sin? α, you can get cosa= 1-2sin? (α/2), we can get 1-cosa=2sin? (α/2), available
Sin? (α/2)=( 1-cosa)/2, available, sin((a/2)= radical sign (1-cosa)/2)cos? (α/2)= 1-sin? (α/2)
So: cos? (α/2) =1-(1-COSA)/2 = (1+COSA)/2 So: cos(a/2)= radical sign (1+COSA)/2 Because: TANA = SINA
So: tan(a/2)=sin(a/2)/cos(a/2)
So: tan(a/2)= radical sign ((1-cosa)/( 1+cosa))
Junior high school mathematics half-angle formula test questions practice