There are many mathematical formulas in junior high school. In order to facilitate everyone to learn the half-angle formula, I sorted out the knowledge points about the half-angle formula in junior high school for your reference.

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