Sin 400 Degrees

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

What is sin 400°?

Answer

sin 400° ≈
0.6428

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

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

sin 400° = sin(400° − 360°) = sin 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 y-axis — sine, y ≈ 0.6428.

+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: sin 40° ≈ 0.6428

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
355°≈ −0.0872
360°0
390°1/2
400°≈ 0.6428
450°1
540°0
570°−1/2

FAQ

What is sin 400°?

sin 400° ≈ 0.6428

Why does sin 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: sin 400° ≈ 0.6428.

Why does a calculator show −0.8509 for sin 400?

The calculator is in radian mode (RAD): it takes sin 400 as the sine of 400 radians, sin 400 rad ≈ −0.8509. Switch it to degrees (DEG): sin 400° ≈ 0.6428. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also