A Brief Review
As a reminder and for quick reference, here is a list of all of the formulae presented by Trig Frog.
The Sum and Difference Formulae
sin(A + B) = sinA cosB + cosA sinB
sin(A - B) = sinA cosB - cosA sinB
cos(A + B) = cosA cosB - sinA sinB
cos(A - B) = cosA cosB + sinA sinB
tan(A + B) = (tanA + tanB)/(1 - tanA tanB)
tan(A - B) = (tan A - tanB)/(1 + tanA tanB)
The Double Angle Formulae
sin2A = 2sinA cosA
cos2A = cos^2 A - sin^2
= 2cos^2 A - 1
= 1 - 2sin^2 A
tan2A = (2tanA)/(1 - tan^2 A)The Power Reduction Formulae
sin^2 A = (1 - cos2A)/2
cos^2 A = (1 + cos2A)/2
tan^2 A = (1 - cos2A)/(1 + cos2A)
The Half Angle Formulae
sin A/2 = ± £((1 - cosA)/2)
cos A/2 = ± £((1 + cosA)/2)
tan A/2 = ± £((1 - cosA)/(1 + cosA))
The Product to Sum Formulae
sinAcosB = 1/2[sin(A + B) + sin(A - B)]
cosAsinB = 1/2[sin(A + B) - sin(A - B)]
cosAcosB = 1/2[cos(A - B) + cos(A + B)]
sinAsinB = 1/2[cos(A - B) - cos(A + B)]
The Sum to Product Formulae
sin x + sin y = 2sin((x + y)/2) cos((x - y)/2)
sin x - sin y = 2cos((x + y)/2) sin((x - y)/2)
cos x + cos y = 2cos((x + y)/2) cos((x - y)/2)
cos x - cos y = -2sin((x + y)/2) sin((x - y)/2)
