Cos 126 Degrees

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

What is cos 126°?

Answer

cos 126° =
−√(10 − 2√5)/4 ≈ −0.5878

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

≈ — rounded to 4 decimal places.

cos 126° = cos(180° − 54°) = −cos 54° = −√(10 − 2√5)/4

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

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

cos 54° = sin 36° = √(1 − cos² 36°) = √(10 − 2√5)/4

xyOP

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

Highlighted: the projection on the x-axis — cosine, x ≈ −0.5878.

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: cos 54° = √(10 − 2√5)/4

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
110°≈ −0.3420
120°−1/2
125°≈ −0.5736
126°−√(10 − 2√5)/4
127°≈ −0.6018
130°≈ −0.6428
134°≈ −0.6947

FAQ

What is cos 126°?

cos 126° = −√(10 − 2√5)/4 ≈ −0.5878

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 0.9440 for cos 126?

The calculator is in radian mode (RAD): it takes cos 126 as the cosine of 126 radians, cos 126 rad ≈ 0.9440. Switch it to degrees (DEG): cos 126° = −√(10 − 2√5)/4 ≈ −0.5878. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also