Sin 324 Degrees

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

What is sin 324°?

Answer

sin 324° =
−√(10 − 2√5)/4 ≈ −0.5878

Angle in radians: 324° = 9π/5. The point of the angle is in quadrant IV, where sine is negative.

≈ — rounded to 4 decimal places.

sin 324° = sin(360° − 36°) = −sin 36° = −√(10 − 2√5)/4

P(cos 324°, sin 324°) = ((√5 + 1)/4, −√(10 − 2√5)/4)

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

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

xyOP

P(cos 324°, sin 324°) ≈ (0.8090, −0.5878)

Highlighted: the projection on the y-axis — sine, y ≈ −0.5878.

All four functions of 324°
FunctionExact valueDecimal
sin 324°−√(10 − 2√5)/4≈ −0.5878
cos 324°(√5 + 1)/4≈ 0.8090
tan 324°−√(5 − 2√5)≈ −0.7265
cot 324°−√(25 + 10√5)/5≈ −1.3764

Reference angle: sin 36° = √(10 − 2√5)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
300°−√3/2
306°−(√5 + 1)/4
315°−√2/2
324°−√(10 − 2√5)/4
330°−1/2
341°≈ −0.3256
342°−(√5 − 1)/4

FAQ

What is sin 324°?

sin 324° = −√(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 −0.4041 for sin 324?

The calculator is in radian mode (RAD): it takes sin 324 as the sine of 324 radians, sin 324 rad ≈ −0.4041. Switch it to degrees (DEG): sin 324° = −√(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