Sin 40 Degrees

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

What is sin 40°?

Answer

sin 40° ≈
0.6428

Angle in radians: 40° = 2π/9. The point of the angle is in quadrant I, where sine is positive.

≈ — rounded to 4 decimal places. sin 40° can't be written with square roots: 40° is not a multiple of 3°.

P(cos 40°, sin 40°) ≈ (0.7660, 0.6428)

xyOP

P(cos 40°, sin 40°) ≈ (0.7660, 0.6428)

Highlighted: the projection on the y-axis — sine, y ≈ 0.6428.

All four functions of 40°
FunctionExact valueDecimal
sin 40°—≈ 0.6428
cos 40°—≈ 0.7660
tan 40°—≈ 0.8391
cot 40°—≈ 1.1918

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
37°≈ 0.6018
38°≈ 0.6157
39°≈ 0.6293
40°≈ 0.6428
41°≈ 0.6561
42°≈ 0.6691
43°≈ 0.6820

FAQ

What is sin 40°?

sin 40° ≈ 0.6428

Why does sin 40° 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°. 40° is not, so no such exact form exists; the value is used as a decimal: sin 40° ≈ 0.6428.

Why does a calculator show 0.7451 for sin 40?

The calculator is in radian mode (RAD): it takes sin 40 as the sine of 40 radians, sin 40 rad ≈ 0.7451. Switch it to degrees (DEG): sin 40° ≈ 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