Sin 540 Degrees

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

What is sin 540°?

Answer

sin 540° =
0

Angle in radians: 540° = 3π. 540° = 360° + 180° — a full turn plus 180°: the point is on the x-axis, (−1, 0).

sin 540° = sin(540° − 360°) = sin 180°

P(cos 540°, sin 540°) = (−1, 0)

xyOP

P(cos 540°, sin 540°) = (−1, 0)

The point lies on the x-axis, so its projection on the y-axis is 0: sin 540° = 0.

+1 turn: the drawing shows 180°.

All four functions of 540°
FunctionExact valueDecimal
sin 540°00
cos 540°−1−1
tan 540°00
cot 540°undefined—

Reference angle: sin 0° = 0

See Also

FAQ

What is sin 540°?

sin 540° = 0

Why is sin 540° equal to 0?

540° ends at the same point as 180°, (−1, 0), and sine is its the y-coordinate, so sin 540° = 0.

Why does a calculator show −0.3466 for sin 540?

The calculator is in radian mode (RAD): it takes sin 540 as the sine of 540 radians, sin 540 rad ≈ −0.3466. Switch it to degrees (DEG): sin 540° = 0. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.