Sin 63 Degrees

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

What is sin 63°?

Answer

sin 63° ≈
0.8910

Angle in radians: 63° = 7π/20. The point of the angle is in quadrant I, where sine is positive.

≈ — rounded to 4 decimal places. An exact form of sin 63° in square roots exists, but it is unwieldy — nested radicals.

P(cos 63°, sin 63°) ≈ (0.4540, 0.8910)

xyOP

P(cos 63°, sin 63°) ≈ (0.4540, 0.8910)

Highlighted: the projection on the y-axis — sine, y ≈ 0.8910.

All four functions of 63°
FunctionExact valueDecimal
sin 63°—≈ 0.8910
cos 63°—≈ 0.4540
tan 63°—≈ 1.9626
cot 63°—≈ 0.5095

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
60°√3/2
61°≈ 0.8746
62°≈ 0.8829
63°≈ 0.8910
64°≈ 0.8988
65°≈ 0.9063
66°≈ 0.9135

FAQ

What is sin 63°?

sin 63° ≈ 0.8910

Is there an exact value of sin 63°?

Yes: 63° 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 63° ≈ 0.8910.

Why does a calculator show 0.1674 for sin 63?

The calculator is in radian mode (RAD): it takes sin 63 as the sine of 63 radians, sin 63 rad ≈ 0.1674. Switch it to degrees (DEG): sin 63° ≈ 0.8910. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also