Tan 5 Degrees

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

What is tan 5°?

Answer

tan 5° ≈
0.0875

Angle in radians: 5° = π/36. The point of the angle is in quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places. tan 5° can't be written with square roots: 5° is not a multiple of 3°.

tan 5° = sin 5° / cos 5° ≈ 0.0875

xyOP

P(cos 5°, sin 5°) ≈ (0.9962, 0.0872)

T(1, tan 5°) ≈ (1, 0.0875) — where line OP meets the line x = 1.

All four functions of 5°
FunctionExact valueDecimal
sin 5°—≈ 0.0872
cos 5°—≈ 0.9962
tan 5°—≈ 0.0875
cot 5°—≈ 11.4301

See Also

FAQ

What is tan 5°?

tan 5° ≈ 0.0875

Why does tan 5° have no exact value?

A trigonometric value of a whole number of degrees can be written with square roots only when the angle is a multiple of 3°. 5° is not, so no such exact form exists; the value is used as a decimal: tan 5° ≈ 0.0875.

Why does a calculator show −3.3805 for tan 5?

The calculator is in radian mode (RAD): it takes tan 5 as the tangent of 5 radians, tan 5 rad ≈ −3.3805. Switch it to degrees (DEG): tan 5° ≈ 0.0875. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.