Cos 306 Degrees

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

What is cos 306°?

Answer

cos 306° =
√(10 − 2√5)/4 ≈ 0.5878

Angle in radians: 306° = 17π/10. The point of the angle is in quadrant IV, where cosine is positive.

≈ — rounded to 4 decimal places.

cos 306° = cos(360° − 54°) = cos 54° = √(10 − 2√5)/4

P(cos 306°, sin 306°) = (√(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 306°, sin 306°) ≈ (0.5878, −0.8090)

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

All four functions of 306°
FunctionExact valueDecimal
sin 306°−(√5 + 1)/4≈ −0.8090
cos 306°√(10 − 2√5)/4≈ 0.5878
tan 306°−√(25 + 10√5)/5≈ −1.3764
cot 306°−√(5 − 2√5)≈ −0.7265

Reference angle: cos 54° = √(10 − 2√5)/4

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
285°(√6 − √2)/4
288°(√5 − 1)/4
300°1/2
306°√(10 − 2√5)/4
315°√2/2
324°(√5 + 1)/4
330°√3/2

FAQ

What is cos 306°?

cos 306° = √(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 −0.3006 for cos 306?

The calculator is in radian mode (RAD): it takes cos 306 as the cosine of 306 radians, cos 306 rad ≈ −0.3006. Switch it to degrees (DEG): cos 306° = √(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