Sin 167 Degrees

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

What is sin 167°?

Answer

sin 167° ≈
0.2250

Angle in radians: 167° = 167π/180. The point of the angle is in quadrant II, where sine is positive.

≈ — rounded to 4 decimal places. sin 167° can't be written with square roots: 167° is not a multiple of 3°.

sin 167° = sin(180° − 13°) = sin 13° ≈ 0.2250

P(cos 167°, sin 167°) ≈ (−0.9744, 0.2250)

xyOP

P(cos 167°, sin 167°) ≈ (−0.9744, 0.2250)

Highlighted: the projection on the y-axis — sine, y ≈ 0.2250.

All four functions of 167°
FunctionExact valueDecimal
sin 167°—≈ 0.2250
cos 167°—≈ −0.9744
tan 167°—≈ −0.2309
cot 167°—≈ −4.3315

Reference angle: sin 13° ≈ 0.2250

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
162°(√5 − 1)/4
164°≈ 0.2756
165°(√6 − √2)/4
167°≈ 0.2250
175°≈ 0.0872
179°≈ 0.0175
180°0

FAQ

What is sin 167°?

sin 167° ≈ 0.2250

Why does sin 167° 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°. 167° is not, so no such exact form exists; the value is used as a decimal: sin 167° ≈ 0.2250.

Why does a calculator show −0.4756 for sin 167?

The calculator is in radian mode (RAD): it takes sin 167 as the sine of 167 radians, sin 167 rad ≈ −0.4756. Switch it to degrees (DEG): sin 167° ≈ 0.2250. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also