Tan 240 Degrees

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

What is tan 240°?

Answer

tan 240° =
√3 ≈ 1.7321

Angle in radians: 240° = 4π/3. The point of the angle is in quadrant III, where tangent is positive.

≈ — rounded to 4 decimal places.

tan 240° = tan(180° + 60°) = tan 60° = √3

tan 240° = sin 240° / cos 240° = (−√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 240°, sin 240°) ≈ (−0.5, −0.8660)

T(1, tan 240°) ≈ (1, 1.7321) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 240°
FunctionExact valueDecimal
sin 240°−√3/2≈ −0.8660
cos 240°−1/2−0.5
tan 240°√3≈ 1.7321
cot 240°√3/3≈ 0.5774

Reference angle: tan 60° = √3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
225°1
227°≈ 1.0724
234°√(25 + 10√5)/5
240°√3
252°√(5 + 2√5)
255°2 + √3
270°undefined

FAQ

What is tan 240°?

tan 240° = √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 240° = √3 ≈ 1.7321.

Why does a calculator show 2.9021 for tan 240?

The calculator is in radian mode (RAD): it takes tan 240 as the tangent of 240 radians, tan 240 rad ≈ 2.9021. Switch it to degrees (DEG): tan 240° = √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