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19 results for “cosine”

Formulae (19)

Law of Cosines

c^2 = a^2 + b^2 - 2ab\cos C

Generalizes Pythagoras to any triangle.

Geometry & TrigonometryIntermediate

Cosine Double Angle

\cos(2\theta) = \cos^2\theta - \sin^2\theta

Double-angle identity for cosine.

Geometry & TrigonometryIntermediate

Tangent Identity

\tan\theta = \frac{\sin\theta}{\cos\theta}

Defines tangent in terms of sine and cosine.

Geometry & TrigonometryIntermediate

Cosine Angle Sum

\cos(A \pm B) = \cos A\cos B \mp \sin A\sin B

Angle addition formula for cosine.

Geometry & TrigonometryIntermediate

Cotangent Identity

\cot\theta = \frac{\cos\theta}{\sin\theta}

Cotangent as the ratio of cosine to sine.

Geometry & TrigonometryBasic

Cofunction Identity

\sin\theta = \cos(90\degree - \theta)

Sine and cosine of complementary angles are equal.

Geometry & TrigonometryBasic

Secant Definition

\sec\theta = \frac{1}{\cos\theta}

Reciprocal of cosine.

TrigonometryBasic

Cosine Ratio (CAH)

\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}

Ratio of the side adjacent to an angle to the hypotenuse.

TrigonometryIntermediate

Secant

\sec\theta = \frac{1}{\cos\theta}

Reciprocal of cosine.

TrigonometryBasic

Tangent Identity

\tan\theta = \frac{\sin\theta}{\cos\theta}

Tangent equals sine divided by cosine.

TrigonometryIntermediate

Cosine of a Sum

\cos(A+B) = \cos A\cos B - \sin A\sin B

Angle addition formula for cosine.

TrigonometryIntermediate

Cosine of a Difference

\cos(A-B) = \cos A\cos B + \sin A\sin B

Angle subtraction formula for cosine.

TrigonometryIntermediate

Double Angle: Cosine

\cos 2\theta = \cos^2\theta - \sin^2\theta

Cosine of twice an angle (also 2cos²θ−1 or 1−2sin²θ).

TrigonometryAdvanced

Half Angle: Cosine

\cos\frac{\theta}{2} = \pm\sqrt{\frac{1+\cos\theta}{2}}

Cosine of half an angle.

TrigonometryIntermediate

Law of Cosines

c^2 = a^2 + b^2 - 2ab\cos C

Generalises Pythagoras to any triangle.

CalculusIntermediate

Derivative of Cosine

\frac{d}{dx}\cos x = -\sin x

Derivative of the cosine function.

CalculusBasic

Derivative of Sine

\frac{d}{dx}\sin x = \cos x

The derivative of sine is cosine.

CalculusBasic

Derivative of Cosine

\frac{d}{dx}\cos x = -\sin x

The derivative of cosine is negative sine.

Data Science & MLIntermediate

Cosine Similarity

\cos\theta = \frac{A \cdot B}{\|A\|\|B\|}

Measures similarity between two vectors by the angle between them.