Tan 167 Degrees

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

What is tan 167°?

Answer

tan 167° ≈
−0.2309

Angle in radians: 167° = 167π/180. The point of the angle is in quadrant II, where tangent is negative.

≈ — rounded to 4 decimal places. tan 167° can't be written with square roots: 167° is not a multiple of 3°.

tan 167° = tan(180° − 13°) = −tan 13° ≈ −0.2309

tan 167° = sin 167° / cos 167° ≈ −0.2309

xyOP

P(cos 167°, sin 167°) ≈ (−0.9744, 0.2250)

T(1, tan 167°) ≈ (1, −0.2309) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 167°
FunctionExact valueDecimal
sin 167°—≈ 0.2250
cos 167°—≈ −0.9744
tan 167°—≈ −0.2309
cot 167°—≈ −4.3315

Reference angle: tan 13° ≈ 0.2309

See Also

FAQ

What is tan 167°?

tan 167° ≈ −0.2309

Why does tan 167° 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°. 167° is not, so no such exact form exists; the value is used as a decimal: tan 167° ≈ −0.2309.

Why does a calculator show 0.5406 for tan 167?

The calculator is in radian mode (RAD): it takes tan 167 as the tangent of 167 radians, tan 167 rad ≈ 0.5406. Switch it to degrees (DEG): tan 167° ≈ −0.2309. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.