Cos 288 Degrees

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

What is cos 288°?

Answer

cos 288° =
(√5 − 1)/4 ≈ 0.3090

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

≈ — rounded to 4 decimal places.

cos 288° = cos(360° − 72°) = cos 72° = (√5 − 1)/4

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

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

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: cos 72° = (√5 − 1)/4

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
255°−(√6 − √2)/4
270°0
285°(√6 − √2)/4
288°(√5 − 1)/4
300°1/2
306°√(10 − 2√5)/4
315°√2/2

FAQ

What is cos 288°?

cos 288° = (√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 0.5178 for cos 288?

The calculator is in radian mode (RAD): it takes cos 288 as the cosine of 288 radians, cos 288 rad ≈ 0.5178. Switch it to degrees (DEG): cos 288° = (√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