Tan 720 Degrees

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

What is tan 720°?

Answer

tan 720° =
0

Angle in radians: 720° = 4π. 720° = 2 · 360° — two full turns: the point is on the x-axis, (1, 0).

tan 720° = tan(720° − 2 · 360°) = tan 0°

tan 720° = sin 720° / cos 720° = 0 / 1 = 0

xyOP

P(cos 720°, sin 720°) = (1, 0)

T(1, tan 720°) = (1, 0) — where line OP meets the line x = 1.

+2 turns: the drawing shows 0°.

All four functions of 720°
FunctionExact valueDecimal
sin 720°00
cos 720°11
tan 720°00
cot 720°undefined—

Reference angle: tan 0° = 0

See Also

FAQ

What is tan 720°?

tan 720° = 0

Why is tan 720° equal to 0?

720° ends at the same point as 0°, (1, 0), and tan = y / x = 0 / 1 = 0.

Why does a calculator show 0.6484 for tan 720?

The calculator is in radian mode (RAD): it takes tan 720 as the tangent of 720 radians, tan 720 rad ≈ 0.6484. Switch it to degrees (DEG): tan 720° = 0. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.