Sin 306 Degrees

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

What is sin 306°?

Answer

sin 306° =
−(√5 + 1)/4 ≈ −0.8090

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

≈ — rounded to 4 decimal places.

sin 306° = sin(360° − 54°) = −sin 54° = −(√5 + 1)/4

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

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

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: sin 54° = (√5 + 1)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

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

FAQ

What is sin 306°?

sin 306° = −(√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 −0.9538 for sin 306?

The calculator is in radian mode (RAD): it takes sin 306 as the sine of 306 radians, sin 306 rad ≈ −0.9538. Switch it to degrees (DEG): sin 306° = −(√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