# Documentation/Calc Functions/TAN

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TAN

Mathematical

## Summary:

Calculates the trigonometric tangent (tan) of an angle expressed in radians.

TAN(Number)

## Returns:

Returns a real number that is the trigonometric tangent of the specified angle.

## Arguments:

Number is a real number, or a reference to a cell containing that number, that is the angle in radians whose trignometric tangent is to be calculated.

• If Number is non-numeric, then TAN reports a #VALUE! error.

If your angle is expressed in degrees, either multiply by PI()/180 or use the RADIANS function to convert to radians.

The formula for the trigonometric tangent of x is:

$\displaystyle{ \tan(x)~=~\frac{1}{\cot(x)}~=~\frac{\sin(x)}{\cos(x)} }$

Mathematically, the tangent of any odd multiple of π/2, i.e. {......-3π/2, -π/2, π/2, 3π/2.....} is undefined. However, because of the inherent inaccuracy in representing π numerically, TAN does not report errors for arguments close to these values. You should be aware that TAN will return large positive or negative results for odd multiples of π/2.

The figure below illustrates the function TAN.

## Examples:

Formula Description Returns
=TAN(1) Trigonometric tangent of 1 radian. 1.5574077246549
=TAN(D1) where cell D1 contains the number -0.5. Trigonometric tangent of -½ radian. 0.54630248984379
=TAN(PI()/4) Trigonometic tangent of π/4 radians. 1
=TAN(RADIANS(45)) Trignometric tangent of 45°, after first converting the angle from degrees to radians. 1
=DEGREES(ATAN(TAN(RADIANS(60))) An angle of 60° is converted to radians, its tangent is taken, then the inverse tangent of that value is calculated, and finally the result is converted back to degrees. 60

TAN