Cot 324 Degrees

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

What is cot 324°?

Answer

cot 324° =
−√(25 + 10√5)/5 ≈ −1.3764

Angle in radians: 324° = 9π/5. The point of the angle is in quadrant IV, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 324° = cot(360° − 36°) = −cot 36° = −√(25 + 10√5)/5

cot 324° = cos 324° / sin 324° = ((√5 + 1)/4) / (−√(10 − 2√5)/4) = −√(25 + 10√5)/5

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

cot 36° = cos 36° / sin 36° = √(25 + 10√5)/5

xyOP

P(cos 324°, sin 324°) ≈ (0.8090, −0.5878)

C(cot 324°, 1) ≈ (−1.3764, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

All four functions of 324°
FunctionExact valueDecimal
sin 324°−√(10 − 2√5)/4≈ −0.5878
cos 324°(√5 + 1)/4≈ 0.8090
tan 324°−√(5 − 2√5)≈ −0.7265
cot 324°−√(25 + 10√5)/5≈ −1.3764

Reference angle: cot 36° = √(25 + 10√5)/5

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
300°−√3/3
306°−√(5 − 2√5)
315°−1
324°−√(25 + 10√5)/5
330°−√3
341°≈ −2.9042
342°−√(5 + 2√5)

FAQ

What is cot 324°?

cot 324° = −√(25 + 10√5)/5 ≈ −1.3764

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 2.2638 for cot 324?

The calculator is in radian mode (RAD): it takes cot 324 as the cotangent of 324 radians, cot 324 rad ≈ 2.2638. Switch it to degrees (DEG): cot 324° = −√(25 + 10√5)/5 ≈ −1.3764. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also