Sin 234 Degrees

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

What is sin 234°?

Answer

sin 234° =
−(√5 + 1)/4 ≈ −0.8090

Angle in radians: 234° = 13π/10. The point of the angle is in quadrant III, where sine is negative.

≈ — rounded to 4 decimal places.

sin 234° = sin(180° + 54°) = −sin 54° = −(√5 + 1)/4

P(cos 234°, sin 234°) = (−√(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 234°, sin 234°) ≈ (−0.5878, −0.8090)

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

All four functions of 234°
FunctionExact valueDecimal
sin 234°−(√5 + 1)/4≈ −0.8090
cos 234°−√(10 − 2√5)/4≈ −0.5878
tan 234°√(25 + 10√5)/5≈ 1.3764
cot 234°√(5 − 2√5)≈ 0.7265

Reference angle: sin 54° = (√5 + 1)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
216°−√(10 − 2√5)/4
225°−√2/2
227°≈ −0.7314
234°−(√5 + 1)/4
240°−√3/2
252°−√(10 + 2√5)/4
255°−(√6 + √2)/4

FAQ

What is sin 234°?

sin 234° = −(√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 0.9988 for sin 234?

The calculator is in radian mode (RAD): it takes sin 234 as the sine of 234 radians, sin 234 rad ≈ 0.9988. Switch it to degrees (DEG): sin 234° = −(√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