Half-angle formulae (HSC SSCE Mathematics Extension 1): Flashcards
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What are half-angle formulae used for?
What are half-angle formulae used for?
To find sine, cosine, and tangent of half angles.
How are half-angle identities derived?
How are half-angle identities derived?
From double angle identities and substitution methods.
What is the formula for sin A using t?
What is the formula for sin A using t?
sin A = 2t / (1 + t^2) where t = tan(A/2).
What is the formula for cos A using t?
What is the formula for cos A using t?
cos A = (1 - t^2) / (1 + t^2) where t = tan(A/2).
How to calculate tan A using t?
How to calculate tan A using t?
tan A = 2t / (1 - t^2) where t = tan(A/2).
What is the value of sin 30 degrees?
What is the value of sin 30 degrees?
sin 30 degrees = 1/2 or 0.5
How to solve 2 cos^2 θ - 1 = 0?
How to solve 2 cos^2 θ - 1 = 0?
Use half-angle formulas for simplification.
What does the half-angle identity help with?
What does the half-angle identity help with?
It simplifies complex integrals like sin^2 x.
What is the half-angle formula for cos(π/8)?
What is the half-angle formula for cos(π/8)?
Use cos(π/4) in the half-angle identity.
What does 1 - cosθ equal using half-angle?
What does 1 - cosθ equal using half-angle?
1 - cosθ = 2sin²(θ/2).