Sin 36 Degrees

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

What is sin 36°?

Answer

sin 36° =
√(10 − 2√5)/4 ≈ 0.5878

Angle in radians: 36° = π/5. The point of the angle is in quadrant I, where sine is positive.

≈ — rounded to 4 decimal places.

P(cos 36°, sin 36°) = ((√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 36°, sin 36°) ≈ (0.8090, 0.5878)

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

All four functions of 36°
FunctionExact valueDecimal
sin 36°√(10 − 2√5)/4≈ 0.5878
cos 36°(√5 + 1)/4≈ 0.8090
tan 36°√(5 − 2√5)≈ 0.7265
cot 36°√(25 + 10√5)/5≈ 1.3764

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
33°≈ 0.5446
34°≈ 0.5592
35°≈ 0.5736
36°√(10 − 2√5)/4
37°≈ 0.6018
38°≈ 0.6157
39°≈ 0.6293

FAQ

What is sin 36°?

sin 36° = √(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 −0.9918 for sin 36?

The calculator is in radian mode (RAD): it takes sin 36 as the sine of 36 radians, sin 36 rad ≈ −0.9918. Switch it to degrees (DEG): sin 36° = √(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