Tan 400 Degrees

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

What is tan 400°?

Answer

tan 400° ≈
0.8391

Angle in radians: 400° = 20π/9. 400° = 360° + 40° — a full turn plus 40°, quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places. tan 400° can't be written with square roots: 400° is not a multiple of 3°.

tan 400° = tan(400° − 360°) = tan 40°

tan 400° = sin 400° / cos 400° ≈ 0.8391

xyOP

P(cos 400°, sin 400°) ≈ (0.7660, 0.6428)

T(1, tan 400°) ≈ (1, 0.8391) — where line OP meets the line x = 1.

+1 turn: the drawing shows 40°.

All four functions of 400°
FunctionExact valueDecimal
sin 400°—≈ 0.6428
cos 400°—≈ 0.7660
tan 400°—≈ 0.8391
cot 400°—≈ 1.1918

Reference angle: tan 40° ≈ 0.8391

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
355°≈ −0.0875
360°0
390°√3/3
400°≈ 0.8391
450°undefined
540°0
570°√3/3

FAQ

What is tan 400°?

tan 400° ≈ 0.8391

Why does tan 400° 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°. 400° is not, so no such exact form exists; the value is used as a decimal: tan 400° ≈ 0.8391.

Why does a calculator show 1.6199 for tan 400?

The calculator is in radian mode (RAD): it takes tan 400 as the tangent of 400 radians, tan 400 rad ≈ 1.6199. Switch it to degrees (DEG): tan 400° ≈ 0.8391. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also