Double-Angle Formulas : The most commonly used multiple-angle formulas. They are used often, so you should learn them.
sin2u = 2sinu cosu
cos 2u = cos^2u - sin^2u
=2cos^2u - 1
=1 - 2sin^2u
tan2u = (2tanu) / ( - tan^2u)
A visual proof for the Double-Angle Formula for Sine:
Power-Reducing Formulas: Can be obtained through the double-angle formulas
Sin^2X = (1-cos2X) / (2)
Cos^2X = (1 + cos2X) / (2)
Tan^2X = (1 - cos2X) / (1 + cos 2X)
Half-Angle Formulas : Can be derived from useful alternative forms of the power-reducing formulas be replacing "X" with (X/2)
Sin (X/2) = +/- * (1 - cosX) / (2)
Cos(X/2) = +/- * (1 + cosX) / (2)
Tan(X/2) = [ (1-cosX) / (sinX) ] = [ (sinX) / (1 + cosX) ]
* = square rooted
-Graphical Representation of a Half-Angle on the
Unit Circle
-I apologize for the lack of "actual" mathematical signs. I received trouble being able to enable the math widget on my computer. I did the best with the recourses at hand.
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