Tan 160 Degrees

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

What is tan 160°?

Answer

tan 160° ≈
−0.3640

Angle in radians: 160° = 8π/9. The point of the angle is in quadrant II, where tangent is negative.

≈ — rounded to 4 decimal places. tan 160° can't be written with square roots: 160° is not a multiple of 3°.

tan 160° = tan(180° − 20°) = −tan 20° ≈ −0.3640

tan 160° = sin 160° / cos 160° ≈ −0.3640

xyOP

P(cos 160°, sin 160°) ≈ (−0.9397, 0.3420)

T(1, tan 160°) ≈ (1, −0.3640) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 160°
FunctionExact valueDecimal
sin 160°—≈ 0.3420
cos 160°—≈ −0.9397
tan 160°—≈ −0.3640
cot 160°—≈ −2.7475

Reference angle: tan 20° ≈ 0.3640

See Also

FAQ

What is tan 160°?

tan 160° ≈ −0.3640

Why does tan 160° 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°. 160° is not, so no such exact form exists; the value is used as a decimal: tan 160° ≈ −0.3640.

Why does a calculator show −0.2249 for tan 160?

The calculator is in radian mode (RAD): it takes tan 160 as the tangent of 160 radians, tan 160 rad ≈ −0.2249. Switch it to degrees (DEG): tan 160° ≈ −0.3640. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.