Tan 159 Degrees

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

What is tan 159°?

Answer

tan 159° ≈
−0.3839

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

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

tan 159° = tan(180° − 21°) = −tan 21° ≈ −0.3839

tan 159° = sin 159° / cos 159° ≈ −0.3839

xyOP

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

T(1, tan 159°) ≈ (1, −0.3839) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

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: tan 21° ≈ 0.3839

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
144°−√(5 − 2√5)
145°≈ −0.7002
150°−√3/3
159°≈ −0.3839
160°≈ −0.3640
162°−√(25 − 10√5)/5
164°≈ −0.2867

FAQ

What is tan 159°?

tan 159° ≈ −0.3839

Is there an exact value of tan 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: tan 159° ≈ −0.3839.

Why does a calculator show −2.7432 for tan 159?

The calculator is in radian mode (RAD): it takes tan 159 as the tangent of 159 radians, tan 159 rad ≈ −2.7432. Switch it to degrees (DEG): tan 159° ≈ −0.3839. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also