Sin 126 Degrees

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

What is sin 126°?

Answer

sin 126° =
(√5 + 1)/4 ≈ 0.8090

Angle in radians: 126° = 7π/10. The point of the angle is in quadrant II, where sine is positive.

≈ — rounded to 4 decimal places.

sin 126° = sin(180° − 54°) = sin 54° = (√5 + 1)/4

P(cos 126°, sin 126°) = (−√(10 − 2√5)/4, (√5 + 1)/4)

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

sin 54° = cos 36° = (√5 + 1)/4

xyOP

P(cos 126°, sin 126°) ≈ (−0.5878, 0.8090)

Highlighted: the projection on the y-axis — sine, y ≈ 0.8090.

All four functions of 126°
FunctionExact valueDecimal
sin 126°(√5 + 1)/4≈ 0.8090
cos 126°−√(10 − 2√5)/4≈ −0.5878
tan 126°−√(25 + 10√5)/5≈ −1.3764
cot 126°−√(5 − 2√5)≈ −0.7265

Reference angle: sin 54° = (√5 + 1)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
110°≈ 0.9397
120°√3/2
125°≈ 0.8192
126°(√5 + 1)/4
127°≈ 0.7986
130°≈ 0.7660
134°≈ 0.7193

FAQ

What is sin 126°?

sin 126° = (√5 + 1)/4 ≈ 0.8090

How are sin 36° and cos 54° related?

They are equal: sin α = cos(90° − α), and 36° + 54° = 90°. So sin 36° = cos 54° = √(10 − 2√5)/4, cos 36° = sin 54° = (√5 + 1)/4, and tan 36° = cot 54° = √(5 − 2√5).

Why does a calculator show 0.3300 for sin 126?

The calculator is in radian mode (RAD): it takes sin 126 as the sine of 126 radians, sin 126 rad ≈ 0.3300. Switch it to degrees (DEG): sin 126° = (√5 + 1)/4 ≈ 0.8090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also