Tan 12 Degrees

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

What is tan 12°?

Answer

tan 12° ≈
0.2126

Angle in radians: 12° = π/15. The point of the angle is in quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places. An exact form of tan 12° in square roots exists, but it is unwieldy — nested radicals.

tan 12° = sin 12° / cos 12° ≈ 0.2126

xyOP

P(cos 12°, sin 12°) ≈ (0.9781, 0.2079)

T(1, tan 12°) ≈ (1, 0.2126) — where line OP meets the line x = 1.

All four functions of 12°
FunctionExact valueDecimal
sin 12°—≈ 0.2079
cos 12°—≈ 0.9781
tan 12°—≈ 0.2126
cot 12°—≈ 4.7046

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
9°≈ 0.1584
10°≈ 0.1763
11°≈ 0.1944
12°≈ 0.2126
13°≈ 0.2309
14°≈ 0.2493
15°2 − √3

FAQ

What is tan 12°?

tan 12° ≈ 0.2126

Is there an exact value of tan 12°?

Yes: 12° 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 12° ≈ 0.2126.

Why does a calculator show −0.6359 for tan 12?

The calculator is in radian mode (RAD): it takes tan 12 as the tangent of 12 radians, tan 12 rad ≈ −0.6359. Switch it to degrees (DEG): tan 12° ≈ 0.2126. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also