Cos 164 Degrees

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

What is cos 164°?

Answer

cos 164° ≈
−0.9613

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

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

cos 164° = cos(180° − 16°) = −cos 16° ≈ −0.9613

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

xyOP

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

Highlighted: the projection on the x-axis — cosine, x ≈ −0.9613.

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: cos 16° ≈ 0.9613

See Also

FAQ

What is cos 164°?

cos 164° ≈ −0.9613

Why does cos 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: cos 164° ≈ −0.9613.

Why does a calculator show 0.8038 for cos 164?

The calculator is in radian mode (RAD): it takes cos 164 as the cosine of 164 radians, cos 164 rad ≈ 0.8038. Switch it to degrees (DEG): cos 164° ≈ −0.9613. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.