Tan 288 Degrees

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

What is tan 288°?

Answer

tan 288° =
−√(5 + 2√5) ≈ −3.0777

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

≈ — rounded to 4 decimal places.

tan 288° = tan(360° − 72°) = −tan 72° = −√(5 + 2√5)

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

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

tan 72° = cot 18° = cos 18° / sin 18° = √(5 + 2√5)

xyOP

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

T(1, tan 288°) ≈ (1, −3.0777) — where line OP meets the line x = 1; T is beyond the drawing, the arrow points to it.

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: tan 72° = √(5 + 2√5)

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
255°2 + √3
270°undefined
285°−2 − √3
288°−√(5 + 2√5)
300°−√3
306°−√(25 + 10√5)/5
315°−1

FAQ

What is tan 288°?

tan 288° = −√(5 + 2√5) ≈ −3.0777

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 −1.6522 for tan 288?

The calculator is in radian mode (RAD): it takes tan 288 as the tangent of 288 radians, tan 288 rad ≈ −1.6522. Switch it to degrees (DEG): tan 288° = −√(5 + 2√5) ≈ −3.0777. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also