Sin 159 Degrees

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

What is sin 159°?

Answer

sin 159° ≈
0.3584

Angle in radians: 159° = 53π/60. The point of the angle is in quadrant II, where sine is positive.

≈ — rounded to 4 decimal places. An exact form of sin 159° in square roots exists, but it is unwieldy — nested radicals.

sin 159° = sin(180° − 21°) = sin 21° ≈ 0.3584

P(cos 159°, sin 159°) ≈ (−0.9336, 0.3584)

xyOP

P(cos 159°, sin 159°) ≈ (−0.9336, 0.3584)

Highlighted: the projection on the y-axis — sine, y ≈ 0.3584.

All four functions of 159°
FunctionExact valueDecimal
sin 159°—≈ 0.3584
cos 159°—≈ −0.9336
tan 159°—≈ −0.3839
cot 159°—≈ −2.6051

Reference angle: sin 21° ≈ 0.3584

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
144°√(10 − 2√5)/4
145°≈ 0.5736
150°1/2
159°≈ 0.3584
160°≈ 0.3420
162°(√5 − 1)/4
164°≈ 0.2756

FAQ

What is sin 159°?

sin 159° ≈ 0.3584

Is there an exact value of sin 159°?

Yes: 159° 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 159° ≈ 0.3584.

Why does a calculator show 0.9395 for sin 159?

The calculator is in radian mode (RAD): it takes sin 159 as the sine of 159 radians, sin 159 rad ≈ 0.9395. Switch it to degrees (DEG): sin 159° ≈ 0.3584. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also