Cot 159 Degrees

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

What is cot 159°?

Answer

cot 159° ≈
−2.6051

Angle in radians: 159° = 53π/60. The point of the angle is in quadrant II, where cotangent is negative.

≈ — rounded to 4 decimal places. An exact form of cot 159° in square roots exists, but it is unwieldy — nested radicals.

cot 159° = cot(180° − 21°) = −cot 21° ≈ −2.6051

cot 159° = cos 159° / sin 159° ≈ −2.6051

xyOP

P(cos 159°, sin 159°) ≈ (−0.9336, 0.3584)

C(cot 159°, 1) ≈ (−2.6051, 1) — where line OP meets the line y = 1; C is beyond the drawing, the arrow points to it.

All four functions of 159°
FunctionExact valueDecimal
sin 159°—≈ 0.3584
cos 159°—≈ −0.9336
tan 159°—≈ −0.3839
cot 159°—≈ −2.6051

Reference angle: cot 21° ≈ 2.6051

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
144°−√(25 + 10√5)/5
145°≈ −1.4281
150°−√3
159°≈ −2.6051
160°≈ −2.7475
162°−√(5 + 2√5)
164°≈ −3.4874

FAQ

What is cot 159°?

cot 159° ≈ −2.6051

Is there an exact value of cot 159°?

Yes: 159° is a multiple of 3°, and the values of such angles can be written with square roots — but the expression is unwieldy, with nested radicals built from the values of 18° and 15° (3° = 18° − 15°). In practice the decimal is used: cot 159° ≈ −2.6051.

Why does a calculator show −0.3645 for cot 159?

The calculator is in radian mode (RAD): it takes cot 159 as the cotangent of 159 radians, cot 159 rad ≈ −0.3645. Switch it to degrees (DEG): cot 159° ≈ −2.6051. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also