Tan 100 Degrees

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

What is tan 100°?

Answer

tan 100° ≈
−5.6713

Angle in radians: 100° = 5π/9. The point of the angle is in quadrant II, where tangent is negative.

≈ — rounded to 4 decimal places. tan 100° can't be written with square roots: 100° is not a multiple of 3°.

tan 100° = tan(180° − 80°) = −tan 80° ≈ −5.6713

tan 100° = sin 100° / cos 100° ≈ −5.6713

xyOP

P(cos 100°, sin 100°) ≈ (−0.1736, 0.9848)

T(1, tan 100°) ≈ (1, −5.6713) — 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 100°
FunctionExact valueDecimal
sin 100°—≈ 0.9848
cos 100°—≈ −0.1736
tan 100°—≈ −5.6713
cot 100°—≈ −0.1763

Reference angle: tan 80° ≈ 5.6713

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
90°undefined
97°≈ −8.1443
98°≈ −7.1154
100°≈ −5.6713
101°≈ −5.1446
105°−2 − √3
106°≈ −3.4874

FAQ

What is tan 100°?

tan 100° ≈ −5.6713

Why does tan 100° 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°. 100° is not, so no such exact form exists; the value is used as a decimal: tan 100° ≈ −5.6713.

Why does a calculator show −0.5872 for tan 100?

The calculator is in radian mode (RAD): it takes tan 100 as the tangent of 100 radians, tan 100 rad ≈ −0.5872. Switch it to degrees (DEG): tan 100° ≈ −5.6713. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also