Cos 72 Degrees

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

What is cos 72°?

Answer

cos 72° =
(√5 − 1)/4 ≈ 0.3090

Angle in radians: 72° = 2π/5. The point of the angle is in quadrant I, where cosine is positive.

≈ — rounded to 4 decimal places.

P(cos 72°, sin 72°) = ((√5 − 1)/4, √(10 + 2√5)/4)

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

cos 72° = 2 cos² 36° − 1 = (√5 − 1)/4

xyOP

P(cos 72°, sin 72°) ≈ (0.3090, 0.9511)

Highlighted: the projection on the x-axis — cosine, x ≈ 0.3090.

All four functions of 72°
FunctionExact valueDecimal
sin 72°√(10 + 2√5)/4≈ 0.9511
cos 72°(√5 − 1)/4≈ 0.3090
tan 72°√(5 + 2√5)≈ 3.0777
cot 72°√(25 − 10√5)/5≈ 0.3249

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
69°≈ 0.3584
70°≈ 0.3420
71°≈ 0.3256
72°(√5 − 1)/4
73°≈ 0.2924
74°≈ 0.2756
75°(√6 − √2)/4

FAQ

What is cos 72°?

cos 72° = (√5 − 1)/4 ≈ 0.3090

How are sin 18° and cos 72° related?

They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

Why does a calculator show −0.9673 for cos 72?

The calculator is in radian mode (RAD): it takes cos 72 as the cosine of 72 radians, cos 72 rad ≈ −0.9673. Switch it to degrees (DEG): cos 72° = (√5 − 1)/4 ≈ 0.3090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also