Sin 390 Degrees

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

What is sin 390°?

Answer

sin 390° =
1/2 = 0.5

Angle in radians: 390° = 13π/6. 390° = 360° + 30° — a full turn plus 30°, quadrant I, where sine is positive.

sin 390° = sin(390° − 360°) = sin 30°

P(cos 390°, sin 390°) = (√3/2, 1/2)

Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

sin 30° = 1/2

xyOP

P(cos 390°, sin 390°) ≈ (0.8660, 0.5)

Highlighted: the projection on the y-axis — sine, y = 0.5.

+1 turn: the drawing shows 30°.

All four functions of 390°
FunctionExact valueDecimal
sin 390°1/20.5
cos 390°√3/2≈ 0.8660
tan 390°√3/3≈ 0.5774
cot 390°√3≈ 1.7321

Reference angle: sin 30° = 1/2

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
345°−(√6 − √2)/4
355°≈ −0.0872
360°0
390°1/2
400°≈ 0.6428
450°1
540°0

FAQ

What is sin 390°?

sin 390° = 1/2 = 0.5

How to remember sin 30°, sin 45° and sin 60°?

Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: sin 390° = 1/2 = 0.5.

Why does a calculator show 0.4282 for sin 390?

The calculator is in radian mode (RAD): it takes sin 390 as the sine of 390 radians, sin 390 rad ≈ 0.4282. Switch it to degrees (DEG): sin 390° = 1/2 = 0.5. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also