How this calculator works
Rearranging the cosine double-angle equations replaces squared functions with first powers at twice the angle. This is useful in integration and in checking trigonometric expressions. Known squared values cannot identify the original sign or quadrant. Value modes therefore report a first-quadrant representative; full-angle mode preserves the supplied angle and function signs.
Formula
sin²x=(1-cos 2x)/2; cos²x=(1+cos 2x)/2; tan²x=(1-cos 2x)/(1+cos 2x), wherever tangent is defined.
Worked example
At 30°, cos 60° = 0.5 gives sin²30° = 0.25 and cos²30° = 0.75. At 45°, the squared sine and cosine are both 0.5 and tan²45° = 1.
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Frequently asked questions
Can a squared sine exceed one?
No. Both sin²x and cos²x lie from 0 to 1. Squared tangent has no finite upper bound.
Why is the original sign lost?
Squaring gives the same result for a value and its negative. A squared input alone cannot select a quadrant.
What happens at 90°?
The squared sine is one, the squared cosine is zero and tangent squared is undefined.