How this calculator works
Cosine starts at one when the angle is zero. It falls to zero at 90°, reaches minus one at 180° and returns to one after a full turn. Its graph is even, so changing the angle’s sign does not change its value. The table helps compare this starting position with sine’s zero crossing. The unscaled cosine has amplitude one; A cos(Bx+C)+D has amplitude |A| and, for non-zero B, period 2π/|B|. Ratio mode uses arccosine from 0° to 180°.
Formula
cos θ = adjacent/hypotenuse = unit-circle x; cos(-θ)=cos θ; cos(θ+2π)=cos θ; cos θ=sin(θ+π/2).
Worked example
cos 60°=1/2 and cos 180°=-1. A unit-circle point at 120° has x=-1/2, so cos 120° is negative despite its positive angle.
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Frequently asked questions
Why does cosine begin at one?
At 0° the unit-circle point is (1,0), so its horizontal coordinate is one.
Is cos(-60°) negative?
No. Cosine is even, so cos(-60°)=cos 60°=0.5.
How is cosine shifted relative to sine?
cos θ=sin(θ+90°). On the usual graph cosine reaches corresponding features one quarter-turn earlier.