Tan 150 Degrees

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

What is tan 150°?

Answer

tan 150° =
−√3/3 ≈ −0.5774

Angle in radians: 150° = 5π/6. The point of the angle is in quadrant II, where tangent is negative.

≈ — rounded to 4 decimal places.

tan 150° = tan(180° − 30°) = −tan 30° = −√3/3

tan 150° = sin 150° / cos 150° = (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 150°, sin 150°) ≈ (−0.8660, 0.5)

T(1, tan 150°) ≈ (1, −0.5774) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 150°
FunctionExact valueDecimal
sin 150°1/20.5
cos 150°−√3/2≈ −0.8660
tan 150°−√3/3≈ −0.5774
cot 150°−√3≈ −1.7321

Reference angle: tan 30° = √3/3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
142°≈ −0.7813
144°−√(5 − 2√5)
145°≈ −0.7002
150°−√3/3
159°≈ −0.3839
160°≈ −0.3640
162°−√(25 − 10√5)/5

FAQ

What is tan 150°?

tan 150° = −√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 150° = −√3/3 ≈ −0.5774.

Why does a calculator show −1.0223 for tan 150?

The calculator is in radian mode (RAD): it takes tan 150 as the tangent of 150 radians, tan 150 rad ≈ −1.0223. Switch it to degrees (DEG): tan 150° = −√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