Sin 285 Degrees

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

What is sin 285°?

Answer

sin 285° =
−(√6 + √2)/4 ≈ −0.9659

Angle in radians: 285° = 19π/12. The point of the angle is in quadrant IV, where sine is negative.

≈ — rounded to 4 decimal places.

sin 285° = sin(360° − 75°) = −sin 75° = −(√6 + √2)/4

P(cos 285°, sin 285°) = ((√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 285°, sin 285°) ≈ (0.2588, −0.9659)

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

All four functions of 285°
FunctionExact valueDecimal
sin 285°−(√6 + √2)/4≈ −0.9659
cos 285°(√6 − √2)/4≈ 0.2588
tan 285°−2 − √3≈ −3.7321
cot 285°√3 − 2≈ −0.2679

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

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
252°−√(10 + 2√5)/4
255°−(√6 + √2)/4
270°−1
285°−(√6 + √2)/4
288°−√(10 + 2√5)/4
300°−√3/2
306°−(√5 + 1)/4

FAQ

What is sin 285°?

sin 285° = −(√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 0.7739 for sin 285?

The calculator is in radian mode (RAD): it takes sin 285 as the sine of 285 radians, sin 285 rad ≈ 0.7739. Switch it to degrees (DEG): sin 285° = −(√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