Cot 198 Degrees

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

What is cot 198°?

Answer

cot 198° =
√(5 + 2√5) ≈ 3.0777

Angle in radians: 198° = 11π/10. The point of the angle is in quadrant III, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 198° = cot(180° + 18°) = cot 18° = √(5 + 2√5)

cot 198° = cos 198° / sin 198° = (−√(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 198°, sin 198°) ≈ (−0.9511, −0.3090)

C(cot 198°, 1) ≈ (3.0777, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed); C is beyond the drawing, the arrow points to it.

All four functions of 198°
FunctionExact valueDecimal
sin 198°−(√5 − 1)/4≈ −0.3090
cos 198°−√(10 + 2√5)/4≈ −0.9511
tan 198°√(25 − 10√5)/5≈ 0.3249
cot 198°√(5 + 2√5)≈ 3.0777

Reference angle: cot 18° = √(5 + 2√5)

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
179°≈ −57.2900
180°undefined
195°2 + √3
198°√(5 + 2√5)
200°≈ 2.7475
210°√3
211°≈ 1.6643

FAQ

What is cot 198°?

cot 198° = √(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 12.5263 for cot 198?

The calculator is in radian mode (RAD): it takes cot 198 as the cotangent of 198 radians, cot 198 rad ≈ 12.5263. Switch it to degrees (DEG): cot 198° = √(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