Trigonometry
Class 11

Compound Angle - Cosine

cos(A+B)=cosAcosBsinAsinB\cos(A+B) = \cos A \cos B - \sin A \sin B
0123456−1−0.500.51
cos(A+B) = cosA×cosB - sinA×sinB

Adjust Variables

Angle A (deg)
A =
0180

Cosine of sum of two angles. Note the minus sign — it's the opposite of the sine formula.

Real-World Applications

Dot product — Vector dot product: A·B = |A||B|cos(θ).

Work calculation — W = F×d×cos(θ); work done by a force at an angle.

Radar systems — Bearing calculations for target tracking.

Crystal optics — Light polarization angle combinations.

Game physics — Collision detection using angle between vectors.

Satellite positioning — Orbital mechanics calculations.

Camera projection — 3D to 2D transformation.

Wind turbines — Optimal blade angle calculations.

Sports analytics — Ball trajectory angle analysis.

Machine learning — Cosine similarity in NLP.

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