Tan 3 Degrees

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

What is tan 3°?

Answer

tan 3° ≈
0.0524

Angle in radians: 3° = π/60. The point of the angle is in quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places. An exact form of tan 3° in square roots exists, but it is unwieldy — nested radicals.

tan 3° = sin 3° / cos 3° ≈ 0.0524

xyOP

P(cos 3°, sin 3°) ≈ (0.9986, 0.0523)

T(1, tan 3°) ≈ (1, 0.0524) — where line OP meets the line x = 1.

All four functions of 3°
FunctionExact valueDecimal
sin 3°—≈ 0.0523
cos 3°—≈ 0.9986
tan 3°—≈ 0.0524
cot 3°—≈ 19.0811

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
0°0
1°≈ 0.0175
2°≈ 0.0349
3°≈ 0.0524
4°≈ 0.0699
5°≈ 0.0875
6°≈ 0.1051

FAQ

What is tan 3°?

tan 3° ≈ 0.0524

Is there an exact value of tan 3°?

Yes: 3° 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 3° ≈ 0.0524.

Why does a calculator show −0.1425 for tan 3?

The calculator is in radian mode (RAD): it takes tan 3 as the tangent of 3 radians, tan 3 rad ≈ −0.1425. Switch it to degrees (DEG): tan 3° ≈ 0.0524. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also