Cot 288 Degrees

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

What is cot 288°?

Answer

cot 288° =
−√(25 − 10√5)/5 ≈ −0.3249

Angle in radians: 288° = 8π/5. The point of the angle is in quadrant IV, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 288° = cot(360° − 72°) = −cot 72° = −√(25 − 10√5)/5

cot 288° = cos 288° / sin 288° = ((√5 − 1)/4) / (−√(10 + 2√5)/4) = −√(25 − 10√5)/5

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

cot 72° = tan 18° = sin 18° / cos 18° = √(25 − 10√5)/5

xyOP

P(cos 288°, sin 288°) ≈ (0.3090, −0.9511)

C(cot 288°, 1) ≈ (−0.3249, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

All four functions of 288°
FunctionExact valueDecimal
sin 288°−√(10 + 2√5)/4≈ −0.9511
cos 288°(√5 − 1)/4≈ 0.3090
tan 288°−√(5 + 2√5)≈ −3.0777
cot 288°−√(25 − 10√5)/5≈ −0.3249

Reference angle: cot 72° = √(25 − 10√5)/5

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
255°2 − √3
270°0
285°√3 − 2
288°−√(25 − 10√5)/5
300°−√3/3
306°−√(5 − 2√5)
315°−1

FAQ

What is cot 288°?

cot 288° = −√(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 −0.6053 for cot 288?

The calculator is in radian mode (RAD): it takes cot 288 as the cotangent of 288 radians, cot 288 rad ≈ −0.6053. Switch it to degrees (DEG): cot 288° = −√(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