Sin 164 Degrees

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

What is sin 164°?

Answer

sin 164° ≈
0.2756

Angle in radians: 164° = 41π/45. The point of the angle is in quadrant II, where sine is positive.

≈ — rounded to 4 decimal places. sin 164° can't be written with square roots: 164° is not a multiple of 3°.

sin 164° = sin(180° − 16°) = sin 16° ≈ 0.2756

P(cos 164°, sin 164°) ≈ (−0.9613, 0.2756)

xyOP

P(cos 164°, sin 164°) ≈ (−0.9613, 0.2756)

Highlighted: the projection on the y-axis — sine, y ≈ 0.2756.

All four functions of 164°
FunctionExact valueDecimal
sin 164°—≈ 0.2756
cos 164°—≈ −0.9613
tan 164°—≈ −0.2867
cot 164°—≈ −3.4874

Reference angle: sin 16° ≈ 0.2756

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
159°≈ 0.3584
160°≈ 0.3420
162°(√5 − 1)/4
164°≈ 0.2756
165°(√6 − √2)/4
167°≈ 0.2250
175°≈ 0.0872

FAQ

What is sin 164°?

sin 164° ≈ 0.2756

Why does sin 164° have no exact value?

A trigonometric value of a whole number of degrees can be written with square roots only when the angle is a multiple of 3°. 164° is not, so no such exact form exists; the value is used as a decimal: sin 164° ≈ 0.2756.

Why does a calculator show 0.5949 for sin 164?

The calculator is in radian mode (RAD): it takes sin 164 as the sine of 164 radians, sin 164 rad ≈ 0.5949. Switch it to degrees (DEG): sin 164° ≈ 0.2756. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also