Double Angles
Prerequisites: Trig equations.

Double angles are useful for when you have sin2x, cos2x, or tan2x. The formulas are as follows:


sin2x = 2sinxcosx

cos2x = cos^2x - sin^2x
cos2x = 2cos^2x - 1
cos2x = 1 - 2sin^2x

tan2x = (2tanx) ÷ (1 - tan^2x)

So you can solve the following equation:

cos2 + cos = 0
2cos^2 - 1 + cos = 0
2cos^2 + cos - 1 = 0
(cos - .5)(cos + 1) = 0

Now you set up two separate equations:

cos - .5 = 0 cos + 1 = 0
cos = .5 cos = -1
= 60°, 240° = 180°

And so:

= 60° + 360°N, 240° + 360°N, 180° + 360°N

Think you're ready? Take the test.
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