How this calculator works
Choose the identity that uses your known ratio. A sine or cosine ratio alone determines the double cosine without choosing a quadrant. It does not determine the sign of the double sine, so ratio modes report only the requested cosine. Angle mode also compares all three square identities. Reverse cosine chooses θ from 0° to 90°; reverse sine uses -45° to 45° and reverse tangent uses angles strictly between those limits.
Formula
cos(2θ) = cos²θ - sin²θ = 2 cos²θ - 1 = 1 - 2 sin²θ = (1 - tan²θ)/(1 + tan²θ).
Worked example
If sin θ = 0.6, cos(2θ) = 1 - 2(0.36) = 0.28. For θ = 30°, the double angle is 60° and its cosine is 0.5.
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Frequently asked questions
Must I first find θ?
No. Use the ratio directly; this also avoids rounding an intermediate inverse angle.
Is cos(2θ) twice cos θ?
No. Doubling an argument differs from multiplying the function value by two.
Why is there just one reverse angle?
Cosine repeats. Each reverse answer halves the principal inverse angle. Other periodic branches also solve the same trigonometric equation.