Sin 360 Degrees

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

What is sin 360°?

Answer

sin 360° =
0

Angle in radians: 360° = 2π. 360° is a full turn: the point is on the x-axis, (1, 0).

sin 360° = sin(360° − 360°) = sin 0°

P(cos 360°, sin 360°) = (1, 0)

xyOP

P(cos 360°, sin 360°) = (1, 0)

The point lies on the x-axis, so its projection on the y-axis is 0: sin 360° = 0.

+1 turn: the drawing shows 0°.

All four functions of 360°
FunctionExact valueDecimal
sin 360°00
cos 360°11
tan 360°00
cot 360°undefined—

Reference angle: sin 0° = 0

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
342°−(√5 − 1)/4
345°−(√6 − √2)/4
355°≈ −0.0872
360°0
390°1/2
400°≈ 0.6428
450°1

FAQ

What is sin 360°?

sin 360° = 0

Why is sin 360° equal to 0?

360° ends at the same point as 0°, (1, 0), and sine is its the y-coordinate, so sin 360° = 0.

Why does a calculator show 0.9589 for sin 360?

The calculator is in radian mode (RAD): it takes sin 360 as the sine of 360 radians, sin 360 rad ≈ 0.9589. Switch it to degrees (DEG): sin 360° = 0. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also