Tan 9 Degrees

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

What is tan 9°?

Answer

tan 9° ≈
0.1584

Angle in radians: 9° = π/20. The point of the angle is in quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places. An exact form of tan 9° in square roots exists, but it is unwieldy — nested radicals.

tan 9° = sin 9° / cos 9° ≈ 0.1584

xyOP

P(cos 9°, sin 9°) ≈ (0.9877, 0.1564)

T(1, tan 9°) ≈ (1, 0.1584) — where line OP meets the line x = 1.

All four functions of 9°
FunctionExact valueDecimal
sin 9°—≈ 0.1564
cos 9°—≈ 0.9877
tan 9°—≈ 0.1584
cot 9°—≈ 6.3138

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
6°≈ 0.1051
7°≈ 0.1228
8°≈ 0.1405
9°≈ 0.1584
10°≈ 0.1763
11°≈ 0.1944
12°≈ 0.2126

FAQ

What is tan 9°?

tan 9° ≈ 0.1584

Is there an exact value of tan 9°?

Yes: 9° 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 9° ≈ 0.1584.

Why does a calculator show −0.4523 for tan 9?

The calculator is in radian mode (RAD): it takes tan 9 as the tangent of 9 radians, tan 9 rad ≈ −0.4523. Switch it to degrees (DEG): tan 9° ≈ 0.1584. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also