Sin 345 Degrees

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

What is sin 345°?

Answer

sin 345° =
−(√6 − √2)/4 ≈ −0.2588

Angle in radians: 345° = 23π/12. The point of the angle is in quadrant IV, where sine is negative.

≈ — rounded to 4 decimal places.

sin 345° = sin(360° − 15°) = −sin 15° = −(√6 − √2)/4

P(cos 345°, sin 345°) = ((√6 + √2)/4, −(√6 − √2)/4)

sin 15° = sin(45° − 30°) = (√2/2)(√3/2) − (√2/2)(1/2) = (√6 − √2)/4

xyOP

P(cos 345°, sin 345°) ≈ (0.9659, −0.2588)

Highlighted: the projection on the y-axis — sine, y ≈ −0.2588.

All four functions of 345°
FunctionExact valueDecimal
sin 345°−(√6 − √2)/4≈ −0.2588
cos 345°(√6 + √2)/4≈ 0.9659
tan 345°√3 − 2≈ −0.2679
cot 345°−2 − √3≈ −3.7321

Reference angle: sin 15° = (√6 − √2)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
330°−1/2
341°≈ −0.3256
342°−(√5 − 1)/4
345°−(√6 − √2)/4
355°≈ −0.0872
360°0
390°1/2

FAQ

What is sin 345°?

sin 345° = −(√6 − √2)/4 ≈ −0.2588

How are sin 15° and cos 75° related?

They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

Why does a calculator show −0.5440 for sin 345?

The calculator is in radian mode (RAD): it takes sin 345 as the sine of 345 radians, sin 345 rad ≈ −0.5440. Switch it to degrees (DEG): sin 345° = −(√6 − √2)/4 ≈ −0.2588. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also