Cos 36 Degrees

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

What is cos 36°?

Answer

cos 36° =
(√5 + 1)/4 ≈ 0.8090

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

xyOP

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

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

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 ↑

Cosine of nearby angles

Anglecos
33°≈ 0.8387
34°≈ 0.8290
35°≈ 0.8192
36°(√5 + 1)/4
37°≈ 0.7986
38°≈ 0.7880
39°≈ 0.7771

FAQ

What is cos 36°?

cos 36° = (√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 −0.1280 for cos 36?

The calculator is in radian mode (RAD): it takes cos 36 as the cosine of 36 radians, cos 36 rad ≈ −0.1280. Switch it to degrees (DEG): cos 36° = (√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