Tan 18 Degrees

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

What is tan 18°?

Answer

tan 18° =
√(25 − 10√5)/5 ≈ 0.3249

Angle in radians: 18° = π/10. The point of the angle is in quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places.

tan 18° = sin 18° / cos 18° = ((√5 − 1)/4) / (√(10 + 2√5)/4) = √(25 − 10√5)/5

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

tan 18° = sin 18° / cos 18° = √(25 − 10√5)/5

xyOP

P(cos 18°, sin 18°) ≈ (0.9511, 0.3090)

T(1, tan 18°) ≈ (1, 0.3249) — where line OP meets the line x = 1.

All four functions of 18°
FunctionExact valueDecimal
sin 18°(√5 − 1)/4≈ 0.3090
cos 18°√(10 + 2√5)/4≈ 0.9511
tan 18°√(25 − 10√5)/5≈ 0.3249
cot 18°√(5 + 2√5)≈ 3.0777

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
15°2 − √3
16°≈ 0.2867
17°≈ 0.3057
18°√(25 − 10√5)/5
19°≈ 0.3443
20°≈ 0.3640
21°≈ 0.3839

FAQ

What is tan 18°?

tan 18° = √(25 − 10√5)/5 ≈ 0.3249

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 −1.1373 for tan 18?

The calculator is in radian mode (RAD): it takes tan 18 as the tangent of 18 radians, tan 18 rad ≈ −1.1373. Switch it to degrees (DEG): tan 18° = √(25 − 10√5)/5 ≈ 0.3249. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also