Tan 210 Degrees

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

What is tan 210°?

Answer

tan 210° =
√3/3 ≈ 0.5774

Angle in radians: 210° = 7π/6. The point of the angle is in quadrant III, where tangent is positive.

≈ — rounded to 4 decimal places.

tan 210° = tan(180° + 30°) = tan 30° = √3/3

tan 210° = sin 210° / cos 210° = (−1/2) / (−√3/2) = √3/3

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

tan 30° = (1/2) / (√3/2) = 1/√3 = √3/3

xyOP

P(cos 210°, sin 210°) ≈ (−0.8660, −0.5)

T(1, tan 210°) ≈ (1, 0.5774) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 210°
FunctionExact valueDecimal
sin 210°−1/2−0.5
cos 210°−√3/2≈ −0.8660
tan 210°√3/3≈ 0.5774
cot 210°√3≈ 1.7321

Reference angle: tan 30° = √3/3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
195°2 − √3
198°√(25 − 10√5)/5
200°≈ 0.3640
210°√3/3
211°≈ 0.6009
215°≈ 0.7002
216°√(5 − 2√5)

FAQ

What is tan 210°?

tan 210° = √3/3 ≈ 0.5774

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 210° = √3/3 ≈ 0.5774.

Why does a calculator show −0.5292 for tan 210?

The calculator is in radian mode (RAD): it takes tan 210 as the tangent of 210 radians, tan 210 rad ≈ −0.5292. Switch it to degrees (DEG): tan 210° = √3/3 ≈ 0.5774. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also