Tan 101 Degrees

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

What is tan 101°?

Answer

tan 101° ≈
−5.1446

Angle in radians: 101° = 101π/180. The point of the angle is in quadrant II, where tangent is negative.

≈ — rounded to 4 decimal places. tan 101° can't be written with square roots: 101° is not a multiple of 3°.

tan 101° = tan(180° − 79°) = −tan 79° ≈ −5.1446

tan 101° = sin 101° / cos 101° ≈ −5.1446

xyOP

P(cos 101°, sin 101°) ≈ (−0.1908, 0.9816)

T(1, tan 101°) ≈ (1, −5.1446) — 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 101°
FunctionExact valueDecimal
sin 101°—≈ 0.9816
cos 101°—≈ −0.1908
tan 101°—≈ −5.1446
cot 101°—≈ −0.1944

Reference angle: tan 79° ≈ 5.1446

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
97°≈ −8.1443
98°≈ −7.1154
100°≈ −5.6713
101°≈ −5.1446
105°−2 − √3
106°≈ −3.4874
108°−√(5 + 2√5)

FAQ

What is tan 101°?

tan 101° ≈ −5.1446

Why does tan 101° 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°. 101° is not, so no such exact form exists; the value is used as a decimal: tan 101° ≈ −5.1446.

Why does a calculator show 0.5068 for tan 101?

The calculator is in radian mode (RAD): it takes tan 101 as the tangent of 101 radians, tan 101 rad ≈ 0.5068. Switch it to degrees (DEG): tan 101° ≈ −5.1446. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also