Sin 162 Degrees

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

What is sin 162°?

Answer

sin 162° =
(√5 − 1)/4 ≈ 0.3090

Angle in radians: 162° = 9π/10. The point of the angle is in quadrant II, where sine is positive.

≈ — rounded to 4 decimal places.

sin 162° = sin(180° − 18°) = sin 18° = (√5 − 1)/4

P(cos 162°, sin 162°) = (−√(10 + 2√5)/4, (√5 − 1)/4)

Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

sin 18° = cos 72° = 2 cos² 36° − 1 = (√5 − 1)/4

xyOP

P(cos 162°, sin 162°) ≈ (−0.9511, 0.3090)

Highlighted: the projection on the y-axis — sine, y ≈ 0.3090.

All four functions of 162°
FunctionExact valueDecimal
sin 162°(√5 − 1)/4≈ 0.3090
cos 162°−√(10 + 2√5)/4≈ −0.9511
tan 162°−√(25 − 10√5)/5≈ −0.3249
cot 162°−√(5 + 2√5)≈ −3.0777

Reference angle: sin 18° = (√5 − 1)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
150°1/2
159°≈ 0.3584
160°≈ 0.3420
162°(√5 − 1)/4
164°≈ 0.2756
165°(√6 − √2)/4
167°≈ 0.2250

FAQ

What is sin 162°?

sin 162° = (√5 − 1)/4 ≈ 0.3090

How are sin 18° and cos 72° related?

They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

Why does a calculator show −0.9785 for sin 162?

The calculator is in radian mode (RAD): it takes sin 162 as the sine of 162 radians, sin 162 rad ≈ −0.9785. Switch it to degrees (DEG): sin 162° = (√5 − 1)/4 ≈ 0.3090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also