Tan 120 Degrees

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

What is tan 120°?

Answer

tan 120° =
−√3 ≈ −1.7321

Angle in radians: 120° = 2π/3. The point of the angle is in quadrant II, where tangent is negative.

≈ — rounded to 4 decimal places.

tan 120° = tan(180° − 60°) = −tan 60° = −√3

tan 120° = sin 120° / cos 120° = (√3/2) / (−1/2) = −√3

Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

tan 60° = (√3/2) / (1/2) = √3

xyOP

P(cos 120°, sin 120°) ≈ (−0.5, 0.8660)

T(1, tan 120°) ≈ (1, −1.7321) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 120°
FunctionExact valueDecimal
sin 120°√3/2≈ 0.8660
cos 120°−1/2−0.5
tan 120°−√3≈ −1.7321
cot 120°−√3/3≈ −0.5774

Reference angle: tan 60° = √3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
106°≈ −3.4874
108°−√(5 + 2√5)
110°≈ −2.7475
120°−√3
125°≈ −1.4281
126°−√(25 + 10√5)/5
127°≈ −1.3270

FAQ

What is tan 120°?

tan 120° = −√3 ≈ −1.7321

How to remember sin 30°, sin 45° and sin 60°?

Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: tan 120° = −√3 ≈ −1.7321.

Why does a calculator show 0.7131 for tan 120?

The calculator is in radian mode (RAD): it takes tan 120 as the tangent of 120 radians, tan 120 rad ≈ 0.7131. Switch it to degrees (DEG): tan 120° = −√3 ≈ −1.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also