Cot 162 Degrees

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

What is cot 162°?

Answer

cot 162° =
−√(5 + 2√5) ≈ −3.0777

Angle in radians: 162° = 9π/10. The point of the angle is in quadrant II, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 162° = cot(180° − 18°) = −cot 18° = −√(5 + 2√5)

cot 162° = cos 162° / sin 162° = (−√(10 + 2√5)/4) / ((√5 − 1)/4) = −√(5 + 2√5)

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

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

xyOP

P(cos 162°, sin 162°) ≈ (−0.9511, 0.3090)

C(cot 162°, 1) ≈ (−3.0777, 1) — where line OP meets the line y = 1; C is beyond the drawing, the arrow points to it.

All four functions of 162°
FunctionExact valueDecimal
sin 162°(√5 − 1)/4≈ 0.3090
cos 162°−√(10 + 2√5)/4≈ −0.9511
tan 162°−√(25 − 10√5)/5≈ −0.3249
cot 162°−√(5 + 2√5)≈ −3.0777

Reference angle: cot 18° = √(5 + 2√5)

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
150°−√3
159°≈ −2.6051
160°≈ −2.7475
162°−√(5 + 2√5)
164°≈ −3.4874
165°−2 − √3
167°≈ −4.3315

FAQ

What is cot 162°?

cot 162° = −√(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 −0.2110 for cot 162?

The calculator is in radian mode (RAD): it takes cot 162 as the cotangent of 162 radians, cot 162 rad ≈ −0.2110. Switch it to degrees (DEG): cot 162° = −√(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