Sin 51 Degrees

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

What is sin 51°?

Answer

sin 51° ≈
0.7771

Angle in radians: 51° = 17π/60. The point of the angle is in quadrant I, where sine is positive.

≈ — rounded to 4 decimal places. An exact form of sin 51° in square roots exists, but it is unwieldy — nested radicals.

P(cos 51°, sin 51°) ≈ (0.6293, 0.7771)

xyOP

P(cos 51°, sin 51°) ≈ (0.6293, 0.7771)

Highlighted: the projection on the y-axis — sine, y ≈ 0.7771.

All four functions of 51°
FunctionExact valueDecimal
sin 51°—≈ 0.7771
cos 51°—≈ 0.6293
tan 51°—≈ 1.2349
cot 51°—≈ 0.8098

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
48°≈ 0.7431
49°≈ 0.7547
50°≈ 0.7660
51°≈ 0.7771
52°≈ 0.7880
53°≈ 0.7986
54°(√5 + 1)/4

FAQ

What is sin 51°?

sin 51° ≈ 0.7771

Is there an exact value of sin 51°?

Yes: 51° is a multiple of 3°, and the values of such angles can be written with square roots — but the expression is unwieldy, with nested radicals built from the values of 18° and 15° (3° = 18° − 15°). In practice the decimal is used: sin 51° ≈ 0.7771.

Why does a calculator show 0.6702 for sin 51?

The calculator is in radian mode (RAD): it takes sin 51 as the sine of 51 radians, sin 51 rad ≈ 0.6702. Switch it to degrees (DEG): sin 51° ≈ 0.7771. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also