Tan 540 Degrees

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

What is tan 540°?

Answer

tan 540° =
0

Angle in radians: 540° = 3π. 540° = 360° + 180° — a full turn plus 180°: the point is on the x-axis, (−1, 0).

tan 540° = tan(540° − 360°) = tan 180°

tan 540° = sin 540° / cos 540° = 0 / (−1) = 0

xyOP

P(cos 540°, sin 540°) = (−1, 0)

T(1, tan 540°) = (1, 0) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

+1 turn: the drawing shows 180°.

All four functions of 540°
FunctionExact valueDecimal
sin 540°00
cos 540°−1−1
tan 540°00
cot 540°undefined—

Reference angle: tan 0° = 0

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
390°√3/3
400°≈ 0.8391
450°undefined
540°0
570°√3/3
690°−√3/3
720°0

FAQ

What is tan 540°?

tan 540° = 0

Why is tan 540° equal to 0?

540° ends at the same point as 180°, (−1, 0), and tan = y / x = 0 / (−1) = 0.

Why does a calculator show −0.3695 for tan 540?

The calculator is in radian mode (RAD): it takes tan 540 as the tangent of 540 radians, tan 540 rad ≈ −0.3695. Switch it to degrees (DEG): tan 540° = 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