Sin 66 Degrees

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

What is sin 66°?

Answer

sin 66° ≈
0.9135

Angle in radians: 66° = 11π/30. The point of the angle is in quadrant I, where sine is positive.

≈ — rounded to 4 decimal places. An exact form of sin 66° in square roots exists, but it is unwieldy — nested radicals.

P(cos 66°, sin 66°) ≈ (0.4067, 0.9135)

xyOP

P(cos 66°, sin 66°) ≈ (0.4067, 0.9135)

Highlighted: the projection on the y-axis — sine, y ≈ 0.9135.

All four functions of 66°
FunctionExact valueDecimal
sin 66°—≈ 0.9135
cos 66°—≈ 0.4067
tan 66°—≈ 2.2460
cot 66°—≈ 0.4452

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
63°≈ 0.8910
64°≈ 0.8988
65°≈ 0.9063
66°≈ 0.9135
67°≈ 0.9205
68°≈ 0.9272
69°≈ 0.9336

FAQ

What is sin 66°?

sin 66° ≈ 0.9135

Is there an exact value of sin 66°?

Yes: 66° 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 66° ≈ 0.9135.

Why does a calculator show −0.0266 for sin 66?

The calculator is in radian mode (RAD): it takes sin 66 as the sine of 66 radians, sin 66 rad ≈ −0.0266. Switch it to degrees (DEG): sin 66° ≈ 0.9135. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also