Cot 165 Degrees

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

What is cot 165°?

Answer

cot 165° =
−2 − √3 ≈ −3.7321

Angle in radians: 165° = 11π/12. The point of the angle is in quadrant II, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 165° = cot(180° − 15°) = −cot 15° = −2 − √3

cot 165° = cos 165° / sin 165° = (−(√6 + √2)/4) / ((√6 − √2)/4) = −2 − √3

cot 15° = 1 / tan 15° = 1 / (2 − √3) = 2 + √3

xyOP

P(cos 165°, sin 165°) ≈ (−0.9659, 0.2588)

C(cot 165°, 1) ≈ (−3.7321, 1) — where line OP meets the line y = 1; C is beyond the drawing, the arrow points to it.

All four functions of 165°
FunctionExact valueDecimal
sin 165°(√6 − √2)/4≈ 0.2588
cos 165°−(√6 + √2)/4≈ −0.9659
tan 165°√3 − 2≈ −0.2679
cot 165°−2 − √3≈ −3.7321

Reference angle: cot 15° = 2 + √3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
160°≈ −2.7475
162°−√(5 + 2√5)
164°≈ −3.4874
165°−2 − √3
167°≈ −4.3315
175°≈ −11.4301
179°≈ −57.2900

FAQ

What is cot 165°?

cot 165° = −2 − √3 ≈ −3.7321

How are sin 15° and cos 75° related?

They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

Why does a calculator show −0.0665 for cot 165?

The calculator is in radian mode (RAD): it takes cot 165 as the cotangent of 165 radians, cot 165 rad ≈ −0.0665. Switch it to degrees (DEG): cot 165° = −2 − √3 ≈ −3.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also