TAN in WPS Spreadsheet: Calculate Tangent, Slopes and Angle Ratios

• Introduced: documented by 2019-05-28 in the official WPS lesson; original introduction is not established.
• Availability: WPS Office for Windows Personal; no numeric release is stated in the edition metadata.
• Scope: exact current supported builds remain unverified. The Windows lesson does not establish equivalent availability in other WPS clients.
• Checked: October 14, 2026 against function-specific documentation. Examples were independently calculated; no native WPS test was performed.

=TAN(number)

The WPS lesson explicitly requires radians. Convert degrees with PI()/180 or RADIANS before calculating. TAN does not inspect a column heading and automatically reinterpret 45 as degrees.

These examples use ordinary real numeric controls away from exact singularities. A theoretically undefined tangent is different from whatever large number or error a specific floating-point build may display.

Put 0, 30, 45, 60 and −45 in A2:A6. In B2 enter and fill down:

=TAN(A2*PI()/180)

Expected results are 0, approximately 0.577350269, 1, approximately 1.732050808, and −1. Negating an angle negates its tangent.

At 45 degrees the two perpendicular triangle legs have equal lengths, giving a ratio of one. That ratio is dimensionless; it is not itself an angle measured in degrees.

A fictional straight segment rises at 12 degrees over a horizontal run of 8 units:

=8*TAN(12*PI()/180)

Expected rise: approximately 1.700452493 units. The tangent is approximately 0.212556562, so the rise is that fraction of the horizontal run.

The run here is the adjacent horizontal leg, not the sloping segment length. If the supplied length instead follows the slope, use a sine-based projection with the appropriate triangle model.

A tangent of 0.08 corresponds to an eight-percent rise/run grade. Its angle is:

=ATAN(0.08)*180/PI()

Expected angle: approximately 4.573921260 degrees. By contrast, a degree angle of eight has tangent approximately 0.140540835, or 14.054083470 percent after multiplying by 100.

Do not enter 8 as though it were both eight degrees and an eight-percent ratio. The input unit and the reporting convention answer different questions. These are mathematical demonstrations, not a design recommendation for any physical installation.

For a 30-degree angle:

=SIN(30*PI()/180)/COS(30*PI()/180)

Expected result: approximately 0.577350269, matching the TAN control. The identity requires a nonzero cosine. It is not a workaround for an angle where tangent is mathematically undefined.

Tangent repeats every pi radians. The 30- and 210-degree controls have the same mathematical tangent, despite pointing in different directions. Retain the original angle when the quadrant matters.

Compare 89 and 91 degrees:

=TAN(89*PI()/180)
=TAN(91*PI()/180)

Expected values are approximately 57.289961631 and −57.289961631. A two-degree change crossing 90 degrees reverses the sign and passes through a singularity; it does not describe a small, smooth change in slope.

The direct WPS lesson does not specify the native outcome at exactly 90 degrees. This guide therefore assigns no error code or infinity result to TAN(PI()/2). A finite approximation to pi/2 can produce a large finite value without making the mathematical tangent defined there.

Check conversion direction, the triangle’s adjacent versus sloping length, and whether the angle is near an odd multiple of 90 degrees. Preserve unrounded inputs when sensitivity matters.

The lesson supports the real tangent definition and unit conversion. Current-build extreme-angle limits, imported text conversion and exact singularity outputs need separate native verification.

• WPS Academy: TAN lesson, 2019-05-28 (Chinese; Windows Personal scope).
• Editorial testing standards.

The direct WPS product lesson supports the stated function scope. Worked outputs are independent expectations, not captured native results or proof of support across all current WPS clients.