Tan 306 Degrees

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

What is tan 306°?

Answer

tan 306° =
−√(25 + 10√5)/5 ≈ −1.3764

Angle in radians: 306° = 17π/10. The point of the angle is in quadrant IV, where tangent is negative.

≈ — rounded to 4 decimal places.

tan 306° = tan(360° − 54°) = −tan 54° = −√(25 + 10√5)/5

tan 306° = sin 306° / cos 306° = (−(√5 + 1)/4) / (√(10 − 2√5)/4) = −√(25 + 10√5)/5

Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

tan 54° = cot 36° = cos 36° / sin 36° = √(25 + 10√5)/5

xyOP

P(cos 306°, sin 306°) ≈ (0.5878, −0.8090)

T(1, tan 306°) ≈ (1, −1.3764) — where line OP meets the line x = 1.

All four functions of 306°
FunctionExact valueDecimal
sin 306°−(√5 + 1)/4≈ −0.8090
cos 306°√(10 − 2√5)/4≈ 0.5878
tan 306°−√(25 + 10√5)/5≈ −1.3764
cot 306°−√(5 − 2√5)≈ −0.7265

Reference angle: tan 54° = √(25 + 10√5)/5

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
285°−2 − √3
288°−√(5 + 2√5)
300°−√3
306°−√(25 + 10√5)/5
315°−1
324°−√(5 − 2√5)
330°−√3/3

FAQ

What is tan 306°?

tan 306° = −√(25 + 10√5)/5 ≈ −1.3764

How are sin 36° and cos 54° related?

They are equal: sin α = cos(90° − α), and 36° + 54° = 90°. So sin 36° = cos 54° = √(10 − 2√5)/4, cos 36° = sin 54° = (√5 + 1)/4, and tan 36° = cot 54° = √(5 − 2√5).

Why does a calculator show 3.1732 for tan 306?

The calculator is in radian mode (RAD): it takes tan 306 as the tangent of 306 radians, tan 306 rad ≈ 3.1732. Switch it to degrees (DEG): tan 306° = −√(25 + 10√5)/5 ≈ −1.3764. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also