Zoho Sheet COT Function: Cotangent, Radians and Distance Examples

• Introduced: The first supported release and original introduction date are not established by the checked sources.
• Current support: Listed in Zoho Sheet’s rolling web-service help, retrieved October 15, 2026. No numbered final functioning version or retirement date is established.
• Platform scope: English-language web documentation; historical clients, mobile and offline parity have not been verified.
• Evidence: Zoho’s COT entry supports the syntax and vendor examples. The additional datasets below are independently calculated mathematical expectations. No formula was executed in native Zoho Sheet for this guide.

COT(angle)

The single required argument is a numeric angle in radians. It may be a literal, expression or cell reference; there are no optional arguments in the documented signature. For degrees, Zoho explicitly gives the conversion angle*PI()/180; RADIANS provides the degree-to-radian helper used here.

COT is a reciprocal trigonometric function, not an inverse function. Mathematically, cot(x) = cos(x)/sin(x) wherever sin(x) is nonzero. ACOT finds an angle from a cotangent value; COTH is the hyperbolic cotangent of a number. Similar names do not make them interchangeable.

The one-argument COT call needs no argument delimiter. These examples use English decimal points. If your spreadsheet uses different decimal punctuation, use the formula editor’s regional convention rather than importing a numeric angle as text with a degree symbol attached.

Create a sheet named CotControls. Put Input_radians in A1 and Cotangent in B1. Enter numeric 0.3 in A2, -0.9 in A3 and the formula =1/2 in A4. Enter =COT(A2) in B2 and fill through B4.

These are Zoho’s published examples, independently recalculated here. Showing nine decimals is a display choice, not a claim that the service stores precisely these rounded numbers. Retain full formula values for later calculations.

Create CotDegrees, reserving A1:E8. Put Degrees, Cotangent, Converted_radians, Identity_check and Difference in A1:E1. Enter the following degree values in A2:A8, then enter these formulas and fill through row 8:

B2: =COT(RADIANS(A2))
C2: =RADIANS(A2)
D2: =COS(C2)/SIN(C2)
E2: =B2-D2

The mathematical difference in E is zero. A small floating-point residual is possible, so compare at an appropriate tolerance rather than requiring bit-for-bit equality. The negative result at 120° is intentional: cosine is negative and sine positive in that quadrant.

Duplicate CotDegrees as ChangedAngle and replace only A4, originally 45, with 30. B4/D4 should now be approximately 1.732050808 instead of 1; C4 becomes approximately 0.523598776. Other rows should be unchanged. This control catches a formula that was accidentally typed with a fixed literal instead of the intended row reference.

Use a separate sheet DistanceEstimate. Put Angle_degrees in A1, Height in B1 and Horizontal_distance in C1. Enter 29, 30 and 31 in A2:A4 and numeric 5 in B2:B4. In C2 enter =B2*COT(RADIANS(A2)) and fill through C4.

Height and distance use the same length unit. The height is the vertical difference between the observation point and the target, and the angle is measured above the horizontal. This is ideal right-triangle geometry, not a field-survey accuracy guarantee.

The three rows bracket a one-degree angle change. They show why a single displayed answer should not imply more accuracy than the measurement supports. Duplicate the sheet and double all three heights to 10: the distances double, with the 30° row becoming approximately 17.320508076. The angle dependence remains nonlinear.

• At mathematical multiples of π, sine is zero and cotangent has no finite value. Exclude those cases from an ordinary finite-result model.
• A stored approximation such as PI() is not exact π. An expression near a pole may produce a large finite value instead of the error you expected. The checked Zoho page does not establish the exact zero/pole error token or large-input precision limits.
• COT(30) means 30 radians. For 30 degrees use COT(RADIANS(30)); multiplying the finished answer by π/180 cannot repair the wrong input units.
• A text label such as 30 degrees is not the numeric input used here. Keep labels separate from numbers and inspect imported cell types.
• In geometry, the adjacent/opposite relationship uses the chosen reference angle. Applying it to a sloping length instead of a vertical height changes the model.

Zoho’s help includes a shared invalid-type/name/reference glossary. It does not provide a complete function-specific truth table for blanks, text coercion, arrays, overflow or singularities. Those cases and exact native error displays remain untested here. If a known literal works but a copied formula fails, check the referenced cell and its units before replacing errors with zero.

Use SIN and COS to inspect the component ratio, RADIANS for degree conversion, and ACOT for the inverse operation. COTH has a different mathematical contract.

The real-number identity is portable mathematics. Function availability, exact errors, numeric limits, locale syntax and import/export behavior must still be checked in the destination spreadsheet; this guide certifies none of those cross-product details.