Sin 72 Degrees

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

What is sin 72°?

Answer

sin 72° =
√(10 + 2√5)/4 ≈ 0.9511

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

sin 72° = cos 18° = √(1 − sin² 18°) = √(10 + 2√5)/4

xyOP

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

Highlighted: the projection on the y-axis — sine, y ≈ 0.9511.

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 ↑

Sine of nearby angles

Anglesin
69°≈ 0.9336
70°≈ 0.9397
71°≈ 0.9455
72°√(10 + 2√5)/4
73°≈ 0.9563
74°≈ 0.9613
75°(√6 + √2)/4

FAQ

What is sin 72°?

sin 72° = √(10 + 2√5)/4 ≈ 0.9511

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 0.2538 for sin 72?

The calculator is in radian mode (RAD): it takes sin 72 as the sine of 72 radians, sin 72 rad ≈ 0.2538. Switch it to degrees (DEG): sin 72° = √(10 + 2√5)/4 ≈ 0.9511. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also