Tan 89 Degrees

Sin, Cos, Tan, Cot of an Angle
Function
Angle (°)

What is tan 89°?

Answer

tan 89° ≈
57.2900

Angle in radians: 89° = 89π/180. The point of the angle is in quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places. tan 89° can't be written with square roots: 89° is not a multiple of 3°.

tan 89° = sin 89° / cos 89° ≈ 57.2900

xyOP

P(cos 89°, sin 89°) ≈ (0.0175, 0.9998)

T(1, tan 89°) ≈ (1, 57.2900) — where line OP meets the line x = 1; T is beyond the drawing, the arrow points to it.

All four functions of 89°
FunctionExact valueDecimal
sin 89°—≈ 0.9998
cos 89°—≈ 0.0175
tan 89°—≈ 57.2900
cot 89°—≈ 0.0175

See Also

FAQ

What is tan 89°?

tan 89° ≈ 57.2900

Why does tan 89° have no exact value?

A trigonometric value of a whole number of degrees can be written with square roots only when the angle is a multiple of 3°. 89° is not, so no such exact form exists; the value is used as a decimal: tan 89° ≈ 57.2900.

Why does a calculator show 1.6858 for tan 89?

The calculator is in radian mode (RAD): it takes tan 89 as the tangent of 89 radians, tan 89 rad ≈ 1.6858. Switch it to degrees (DEG): tan 89° ≈ 57.2900. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.