Tan 110 Degrees

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

What is tan 110°?

Answer

tan 110° ≈
−2.7475

Angle in radians: 110° = 11π/18. The point of the angle is in quadrant II, where tangent is negative.

≈ — rounded to 4 decimal places. tan 110° can't be written with square roots: 110° is not a multiple of 3°.

tan 110° = tan(180° − 70°) = −tan 70° ≈ −2.7475

tan 110° = sin 110° / cos 110° ≈ −2.7475

xyOP

P(cos 110°, sin 110°) ≈ (−0.3420, 0.9397)

T(1, tan 110°) ≈ (1, −2.7475) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed); T is beyond the drawing, the arrow points to it.

All four functions of 110°
FunctionExact valueDecimal
sin 110°—≈ 0.9397
cos 110°—≈ −0.3420
tan 110°—≈ −2.7475
cot 110°—≈ −0.3640

Reference angle: tan 70° ≈ 2.7475

See Also

FAQ

What is tan 110°?

tan 110° ≈ −2.7475

Why does tan 110° 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°. 110° is not, so no such exact form exists; the value is used as a decimal: tan 110° ≈ −2.7475.

Why does a calculator show 0.0443 for tan 110?

The calculator is in radian mode (RAD): it takes tan 110 as the tangent of 110 radians, tan 110 rad ≈ 0.0443. Switch it to degrees (DEG): tan 110° ≈ −2.7475. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.