Sin 255 Degrees

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

What is sin 255°?

Answer

sin 255° =
−(√6 + √2)/4 ≈ −0.9659

Angle in radians: 255° = 17π/12. The point of the angle is in quadrant III, where sine is negative.

≈ — rounded to 4 decimal places.

sin 255° = sin(180° + 75°) = −sin 75° = −(√6 + √2)/4

P(cos 255°, sin 255°) = (−(√6 − √2)/4, −(√6 + √2)/4)

sin 75° = sin(45° + 30°) = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4

xyOP

P(cos 255°, sin 255°) ≈ (−0.2588, −0.9659)

Highlighted: the projection on the y-axis — sine, y ≈ −0.9659.

All four functions of 255°
FunctionExact valueDecimal
sin 255°−(√6 + √2)/4≈ −0.9659
cos 255°−(√6 − √2)/4≈ −0.2588
tan 255°2 + √3≈ 3.7321
cot 255°2 − √3≈ 0.2679

Reference angle: sin 75° = (√6 + √2)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
234°−(√5 + 1)/4
240°−√3/2
252°−√(10 + 2√5)/4
255°−(√6 + √2)/4
270°−1
285°−(√6 + √2)/4
288°−√(10 + 2√5)/4

FAQ

What is sin 255°?

sin 255° = −(√6 + √2)/4 ≈ −0.9659

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 −0.5064 for sin 255?

The calculator is in radian mode (RAD): it takes sin 255 as the sine of 255 radians, sin 255 rad ≈ −0.5064. Switch it to degrees (DEG): sin 255° = −(√6 + √2)/4 ≈ −0.9659. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also