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Trigonometric Identities
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Trigonometric identities including \(\sin^2\theta+\cos^2\theta=1\), \(\sin2\theta=2\sin\theta\cos\theta\), and the equivalent forms of \(\cos2\theta\): \(\cos^2\theta-\sin^2\theta\), \(2\cos^2\theta-1\), and \(1-2\sin^2\theta\).
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sin²θ+cos²θ=1
SL 3.6
For any value of θ:
sin2θ+cos2θ=1📖
Sine Double Angle Identity
SL 3.6
The double angle identity for sin states that
sin2θ=2sinθcosθ📖
Cosine Double Angle Identity
SL 3.6
The double angle identity for cosine states that
cos2θ =cos2θ−sin2θ=2cos2θ−1=1−2sin2θ
These three different forms come from leveraging sin2θ+cos2θ=1.
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