Sin 144 Degrees

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

What is sin 144°?

Answer

sin 144° =
√(10 − 2√5)/4 ≈ 0.5878

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

≈ — rounded to 4 decimal places.

sin 144° = sin(180° − 36°) = sin 36° = √(10 − 2√5)/4

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

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

sin 36° = √(1 − cos² 36°) = √(10 − 2√5)/4

xyOP

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

Highlighted: the projection on the y-axis — sine, y ≈ 0.5878.

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: sin 36° = √(10 − 2√5)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
135°√2/2
140°≈ 0.6428
142°≈ 0.6157
144°√(10 − 2√5)/4
145°≈ 0.5736
150°1/2
159°≈ 0.3584

FAQ

What is sin 144°?

sin 144° = √(10 − 2√5)/4 ≈ 0.5878

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 −0.4910 for sin 144?

The calculator is in radian mode (RAD): it takes sin 144 as the sine of 144 radians, sin 144 rad ≈ −0.4910. Switch it to degrees (DEG): sin 144° = √(10 − 2√5)/4 ≈ 0.5878. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also