Tan 360 Degrees

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

What is tan 360°?

Answer

tan 360° =
0

Angle in radians: 360° = 2π. 360° is a full turn: the point is on the x-axis, (1, 0).

tan 360° = tan(360° − 360°) = tan 0°

tan 360° = sin 360° / cos 360° = 0 / 1 = 0

xyOP

P(cos 360°, sin 360°) = (1, 0)

T(1, tan 360°) = (1, 0) — where line OP meets the line x = 1.

+1 turn: the drawing shows 0°.

All four functions of 360°
FunctionExact valueDecimal
sin 360°00
cos 360°11
tan 360°00
cot 360°undefined—

Reference angle: tan 0° = 0

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
342°−√(25 − 10√5)/5
345°√3 − 2
355°≈ −0.0875
360°0
390°√3/3
400°≈ 0.8391
450°undefined

FAQ

What is tan 360°?

tan 360° = 0

Why is tan 360° equal to 0?

360° ends at the same point as 0°, (1, 0), and tan = y / x = 0 / 1 = 0.

Why does a calculator show −3.3801 for tan 360?

The calculator is in radian mode (RAD): it takes tan 360 as the tangent of 360 radians, tan 360 rad ≈ −3.3801. Switch it to degrees (DEG): tan 360° = 0. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also