Cos 400 Degrees

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

What is cos 400°?

Answer

cos 400° ≈
0.7660

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

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

cos 400° = cos(400° − 360°) = cos 40°

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

xyOP

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

Highlighted: the projection on the x-axis — cosine, x ≈ 0.7660.

+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: cos 40° ≈ 0.7660

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
355°≈ 0.9962
360°1
390°√3/2
400°≈ 0.7660
450°0
540°−1
570°−√3/2

FAQ

What is cos 400°?

cos 400° ≈ 0.7660

Why does cos 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: cos 400° ≈ 0.7660.

Why does a calculator show −0.5253 for cos 400?

The calculator is in radian mode (RAD): it takes cos 400 as the cosine of 400 radians, cos 400 rad ≈ −0.5253. Switch it to degrees (DEG): cos 400° ≈ 0.7660. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also