Cot 342 Degrees

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

What is cot 342°?

Answer

cot 342° =
−√(5 + 2√5) ≈ −3.0777

Angle in radians: 342° = 19π/10. The point of the angle is in quadrant IV, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 342° = cot(360° − 18°) = −cot 18° = −√(5 + 2√5)

cot 342° = cos 342° / sin 342° = (√(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 342°, sin 342°) ≈ (0.9511, −0.3090)

C(cot 342°, 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 342°
FunctionExact valueDecimal
sin 342°−(√5 − 1)/4≈ −0.3090
cos 342°√(10 + 2√5)/4≈ 0.9511
tan 342°−√(25 − 10√5)/5≈ −0.3249
cot 342°−√(5 + 2√5)≈ −3.0777

Reference angle: cot 18° = √(5 + 2√5)

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
324°−√(25 + 10√5)/5
330°−√3
341°≈ −2.9042
342°−√(5 + 2√5)
345°−2 − √3
355°≈ −11.4301
360°undefined

FAQ

What is cot 342°?

cot 342° = −√(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 −2.1599 for cot 342?

The calculator is in radian mode (RAD): it takes cot 342 as the cotangent of 342 radians, cot 342 rad ≈ −2.1599. Switch it to degrees (DEG): cot 342° = −√(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