Tan 285 Degrees

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

What is tan 285°?

Answer

tan 285° =
−2 − √3 ≈ −3.7321

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

≈ — rounded to 4 decimal places.

tan 285° = tan(360° − 75°) = −tan 75° = −2 − √3

tan 285° = sin 285° / cos 285° = (−(√6 + √2)/4) / ((√6 − √2)/4) = −2 − √3

tan 75° = tan(45° + 30°) = (1 + √3/3) / (1 − √3/3) = 2 + √3

xyOP

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

T(1, tan 285°) ≈ (1, −3.7321) — where line OP meets the line x = 1; T is beyond the drawing, the arrow points to it.

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: tan 75° = 2 + √3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
252°√(5 + 2√5)
255°2 + √3
270°undefined
285°−2 − √3
288°−√(5 + 2√5)
300°−√3
306°−√(25 + 10√5)/5

FAQ

What is tan 285°?

tan 285° = −2 − √3 ≈ −3.7321

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 −1.2219 for tan 285?

The calculator is in radian mode (RAD): it takes tan 285 as the tangent of 285 radians, tan 285 rad ≈ −1.2219. Switch it to degrees (DEG): tan 285° = −2 − √3 ≈ −3.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also