Sin 342 Degrees

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

What is sin 342°?

Answer

sin 342° =
−(√5 − 1)/4 ≈ −0.3090

Angle in radians: 342° = 19π/10. The point of the angle is in quadrant IV, where sine is negative.

≈ — rounded to 4 decimal places.

sin 342° = sin(360° − 18°) = −sin 18° = −(√5 − 1)/4

P(cos 342°, sin 342°) = (√(10 + 2√5)/4, −(√5 − 1)/4)

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

sin 18° = cos 72° = 2 cos² 36° − 1 = (√5 − 1)/4

xyOP

P(cos 342°, sin 342°) ≈ (0.9511, −0.3090)

Highlighted: the projection on the y-axis — sine, y ≈ −0.3090.

All four functions of 342°
FunctionExact valueDecimal
sin 342°−(√5 − 1)/4≈ −0.3090
cos 342°√(10 + 2√5)/4≈ 0.9511
tan 342°−√(25 − 10√5)/5≈ −0.3249
cot 342°−√(5 + 2√5)≈ −3.0777

Reference angle: sin 18° = (√5 − 1)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
324°−√(10 − 2√5)/4
330°−1/2
341°≈ −0.3256
342°−(√5 − 1)/4
345°−(√6 − √2)/4
355°≈ −0.0872
360°0

FAQ

What is sin 342°?

sin 342° = −(√5 − 1)/4 ≈ −0.3090

How are sin 18° and cos 72° related?

They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

Why does a calculator show 0.4201 for sin 342?

The calculator is in radian mode (RAD): it takes sin 342 as the sine of 342 radians, sin 342 rad ≈ 0.4201. Switch it to degrees (DEG): sin 342° = −(√5 − 1)/4 ≈ −0.3090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also