Q: Do tangent functions have amplitudes

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The tangent.

The basic functions of trigonometry are: sine cosine tangent secant cosecant cotangent

tangent, cosecants, secant, cotangent.

sine, cosine, tangent, cosecant, secant and cotangent.

Sine, Cosine, Tangent, Cotangent, secant and cosecant

They are different trigonometric functions!

The tangent and cotangent functions.

Sine Cosine Tangent ArcSine ArcCosine ArcTangent

You can use your trigonometric functions (sine, cosine, and tangent).

The six basic functions of trigonometry are the sine, cosine, tangent, cosecant, secant, and cotangent functions. Abbreviated sin, cos, tan, csc, sec, cot.

The range of the circular trig functions sin and cos is is [-1,1], but even in the case of circular functions the range of the tangent function is all real numbers. This is of course true of tangent even if we do not limit it to circular functions. So your question, I assume, is asking about all trig functions. If so the range is all real numbers.

An arctangent is any of several single-valued or multivalued functions which are inverses of the tangent function.