Tan 300 Degrees

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

What is tan 300°?

Answer

tan 300° =
−√3 ≈ −1.7321

Angle in radians: 300° = 5π/3. The point of the angle is in quadrant IV, where tangent is negative.

≈ — rounded to 4 decimal places.

tan 300° = tan(360° − 60°) = −tan 60° = −√3

tan 300° = sin 300° / cos 300° = (−√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 300°, sin 300°) ≈ (0.5, −0.8660)

T(1, tan 300°) ≈ (1, −1.7321) — where line OP meets the line x = 1.

All four functions of 300°
FunctionExact valueDecimal
sin 300°−√3/2≈ −0.8660
cos 300°1/20.5
tan 300°−√3≈ −1.7321
cot 300°−√3/3≈ −0.5774

Reference angle: tan 60° = √3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
270°undefined
285°−2 − √3
288°−√(5 + 2√5)
300°−√3
306°−√(25 + 10√5)/5
315°−1
324°−√(5 − 2√5)

FAQ

What is tan 300°?

tan 300° = −√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 300° = −√3 ≈ −1.7321.

Why does a calculator show 45.2447 for tan 300?

The calculator is in radian mode (RAD): it takes tan 300 as the tangent of 300 radians, tan 300 rad ≈ 45.2447. Switch it to degrees (DEG): tan 300° = −√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