Tan 36 Degrees

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

What is tan 36°?

Answer

tan 36° =
√(5 − 2√5) ≈ 0.7265

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

≈ — rounded to 4 decimal places.

tan 36° = sin 36° / cos 36° = (√(10 − 2√5)/4) / ((√5 + 1)/4) = √(5 − 2√5)

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

tan 36° = sin 36° / cos 36° = √(5 − 2√5)

xyOP

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

T(1, tan 36°) ≈ (1, 0.7265) — where line OP meets the line x = 1.

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 ↑

Tangent of nearby angles

Angletan
33°≈ 0.6494
34°≈ 0.6745
35°≈ 0.7002
36°√(5 − 2√5)
37°≈ 0.7536
38°≈ 0.7813
39°≈ 0.8098

FAQ

What is tan 36°?

tan 36° = √(5 − 2√5) ≈ 0.7265

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 7.7505 for tan 36?

The calculator is in radian mode (RAD): it takes tan 36 as the tangent of 36 radians, tan 36 rad ≈ 7.7505. Switch it to degrees (DEG): tan 36° = √(5 − 2√5) ≈ 0.7265. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also