Tan 330 Degrees

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

What is tan 330°?

Answer

tan 330° =
−√3/3 ≈ −0.5774

Angle in radians: 330° = 11π/6. The point of the angle is in quadrant IV, where tangent is negative.

≈ — rounded to 4 decimal places.

tan 330° = tan(360° − 30°) = −tan 30° = −√3/3

tan 330° = sin 330° / cos 330° = (−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 330°, sin 330°) ≈ (0.8660, −0.5)

T(1, tan 330°) ≈ (1, −0.5774) — where line OP meets the line x = 1.

All four functions of 330°
FunctionExact valueDecimal
sin 330°−1/2−0.5
cos 330°√3/2≈ 0.8660
tan 330°−√3/3≈ −0.5774
cot 330°−√3≈ −1.7321

Reference angle: tan 30° = √3/3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
306°−√(25 + 10√5)/5
315°−1
324°−√(5 − 2√5)
330°−√3/3
341°≈ −0.3443
342°−√(25 − 10√5)/5
345°√3 − 2

FAQ

What is tan 330°?

tan 330° = −√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 330° = −√3/3 ≈ −0.5774.

Why does a calculator show 0.1336 for tan 330?

The calculator is in radian mode (RAD): it takes tan 330 as the tangent of 330 radians, tan 330 rad ≈ 0.1336. Switch it to degrees (DEG): tan 330° = −√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