Tan 144 Degrees

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

What is tan 144°?

Answer

tan 144° =
−√(5 − 2√5) ≈ −0.7265

Angle in radians: 144° = 4π/5. The point of the angle is in quadrant II, where tangent is negative.

≈ — rounded to 4 decimal places.

tan 144° = tan(180° − 36°) = −tan 36° = −√(5 − 2√5)

tan 144° = sin 144° / cos 144° = (√(10 − 2√5)/4) / (−(√5 + 1)/4) = −√(5 − 2√5)

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

tan 36° = sin 36° / cos 36° = √(5 − 2√5)

xyOP

P(cos 144°, sin 144°) ≈ (−0.8090, 0.5878)

T(1, tan 144°) ≈ (1, −0.7265) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 144°
FunctionExact valueDecimal
sin 144°√(10 − 2√5)/4≈ 0.5878
cos 144°−(√5 + 1)/4≈ −0.8090
tan 144°−√(5 − 2√5)≈ −0.7265
cot 144°−√(25 + 10√5)/5≈ −1.3764

Reference angle: tan 36° = √(5 − 2√5)

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
135°−1
140°≈ −0.8391
142°≈ −0.7813
144°−√(5 − 2√5)
145°≈ −0.7002
150°−√3/3
159°≈ −0.3839

FAQ

What is tan 144°?

tan 144° = −√(5 − 2√5) ≈ −0.7265

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 −0.5636 for tan 144?

The calculator is in radian mode (RAD): it takes tan 144 as the tangent of 144 radians, tan 144 rad ≈ −0.5636. Switch it to degrees (DEG): tan 144° = −√(5 − 2√5) ≈ −0.7265. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also