Cos 360 Degrees

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

What is cos 360°?

Answer

cos 360° =
1

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

cos 360° = cos(360° − 360°) = cos 0°

P(cos 360°, sin 360°) = (1, 0)

xyOP

P(cos 360°, sin 360°) = (1, 0)

Highlighted: the projection on the x-axis — cosine, x = 1.

+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: cos 0° = 1

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
342°√(10 + 2√5)/4
345°(√6 + √2)/4
355°≈ 0.9962
360°1
390°√3/2
400°≈ 0.7660
450°0

FAQ

What is cos 360°?

cos 360° = 1

Why is cos 360° equal to 1?

360° ends at the same point as 0°, (1, 0), and cosine is its the x-coordinate, so cos 360° = 1.

Why does a calculator show −0.2837 for cos 360?

The calculator is in radian mode (RAD): it takes cos 360 as the cosine of 360 radians, cos 360 rad ≈ −0.2837. Switch it to degrees (DEG): cos 360° = 1. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also