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14 results for “tangent”

Formulae (14)

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

Defines tangent in terms of sine and cosine.

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

Cotangent as the ratio of cosine to sine.

\tan(2\theta) = \frac{2\tan\theta}{1 - \tan^2\theta}

Double-angle identity for tangent.

\tan\frac{\theta}{2} = \frac{1-\cos\theta}{\sin\theta}

Expresses the tangent of a half angle.

\tan\theta = \frac{\text{opposite}}{\text{adjacent}}

Ratio of the opposite side to the adjacent side.

\cot\theta = \frac{1}{\tan\theta} = \frac{\cos\theta}{\sin\theta}

Reciprocal of tangent.

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

Tangent equals sine divided by cosine.

\tan(A+B) = \frac{\tan A + \tan B}{1 - \tan A\tan B}

Angle addition formula for tangent.

\tan(A-B) = \frac{\tan A - \tan B}{1 + \tan A\tan B}

Angle subtraction formula for tangent.

\tan 2\theta = \frac{2\tan\theta}{1 - \tan^2\theta}

Tangent of twice an angle.

\tan\frac{\theta}{2} = \frac{1-\cos\theta}{\sin\theta}

Tangent of half an angle.

\frac{a-b}{a+b} = \frac{\tan\tfrac{A-B}{2}}{\tan\tfrac{A+B}{2}}

Relates two sides and their opposite angles.

\frac{d}{dx}\tan x = \sec^2 x

Derivative of the tangent function.

f'(c) = \frac{f(b)-f(a)}{b-a}

Guarantees a point where the tangent equals the average slope.