Tan 180 Degrees

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

What is tan 180°?

Answer

tan 180° =
0

Angle in radians: 180° = π. The point of the angle is on the x-axis: (−1, 0).

tan 180° = sin 180° / cos 180° = 0 / (−1) = 0

xyOP

P(cos 180°, sin 180°) = (−1, 0)

T(1, tan 180°) = (1, 0) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 180°
FunctionExact valueDecimal
sin 180°00
cos 180°−1−1
tan 180°00
cot 180°undefined—

Reference angle: tan 0° = 0

See Also

FAQ

What is tan 180°?

tan 180° = 0

Why is tan 180° equal to 0?

The point of 180° on the unit circle is (−1, 0), and tan = y / x = 0 / (−1) = 0.

Why does a calculator show 1.3387 for tan 180?

The calculator is in radian mode (RAD): it takes tan 180 as the tangent of 180 radians, tan 180 rad ≈ 1.3387. Switch it to degrees (DEG): tan 180° = 0. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.