Tan 85 Degrees

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

What is tan 85°?

Answer

tan 85° ≈
11.4301

Angle in radians: 85° = 17π/36. The point of the angle is in quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places. tan 85° can't be written with square roots: 85° is not a multiple of 3°.

tan 85° = sin 85° / cos 85° ≈ 11.4301

xyOP

P(cos 85°, sin 85°) ≈ (0.0872, 0.9962)

T(1, tan 85°) ≈ (1, 11.4301) — where line OP meets the line x = 1; T is beyond the drawing, the arrow points to it.

All four functions of 85°
FunctionExact valueDecimal
sin 85°—≈ 0.9962
cos 85°—≈ 0.0872
tan 85°—≈ 11.4301
cot 85°—≈ 0.0875

See Also

FAQ

What is tan 85°?

tan 85° ≈ 11.4301

Why does tan 85° 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°. 85° is not, so no such exact form exists; the value is used as a decimal: tan 85° ≈ 11.4301.

Why does a calculator show 0.1789 for tan 85?

The calculator is in radian mode (RAD): it takes tan 85 as the tangent of 85 radians, tan 85 rad ≈ 0.1789. Switch it to degrees (DEG): tan 85° ≈ 11.4301. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.