Cos 144 Degrees

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

What is cos 144°?

Answer

cos 144° =
−(√5 + 1)/4 ≈ −0.8090

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

≈ — rounded to 4 decimal places.

cos 144° = cos(180° − 36°) = −cos 36° = −(√5 + 1)/4

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

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

xyOP

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

Highlighted: the projection on the x-axis — cosine, x ≈ −0.8090.

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: cos 36° = (√5 + 1)/4

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
135°−√2/2
140°≈ −0.7660
142°≈ −0.7880
144°−(√5 + 1)/4
145°≈ −0.8192
150°−√3/2
159°≈ −0.9336

FAQ

What is cos 144°?

cos 144° = −(√5 + 1)/4 ≈ −0.8090

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 0.8711 for cos 144?

The calculator is in radian mode (RAD): it takes cos 144 as the cosine of 144 radians, cos 144 rad ≈ 0.8711. Switch it to degrees (DEG): cos 144° = −(√5 + 1)/4 ≈ −0.8090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also