Sin 9 Degrees

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

What is sin 9°?

Answer

sin 9° ≈
0.1564

Angle in radians: 9° = π/20. The point of the angle is in quadrant I, where sine is positive.

≈ — rounded to 4 decimal places. An exact form of sin 9° in square roots exists, but it is unwieldy — nested radicals.

P(cos 9°, sin 9°) ≈ (0.9877, 0.1564)

xyOP

P(cos 9°, sin 9°) ≈ (0.9877, 0.1564)

Highlighted: the projection on the y-axis — sine, y ≈ 0.1564.

All four functions of 9°
FunctionExact valueDecimal
sin 9°—≈ 0.1564
cos 9°—≈ 0.9877
tan 9°—≈ 0.1584
cot 9°—≈ 6.3138

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
6°≈ 0.1045
7°≈ 0.1219
8°≈ 0.1392
9°≈ 0.1564
10°≈ 0.1736
11°≈ 0.1908
12°≈ 0.2079

FAQ

What is sin 9°?

sin 9° ≈ 0.1564

Is there an exact value of sin 9°?

Yes: 9° 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 9° ≈ 0.1564.

Why does a calculator show 0.4121 for sin 9?

The calculator is in radian mode (RAD): it takes sin 9 as the sine of 9 radians, sin 9 rad ≈ 0.4121. Switch it to degrees (DEG): sin 9° ≈ 0.1564. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also