Tan 255 Degrees

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

What is tan 255°?

Answer

tan 255° =
2 + √3 ≈ 3.7321

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

≈ — rounded to 4 decimal places.

tan 255° = tan(180° + 75°) = tan 75° = 2 + √3

tan 255° = sin 255° / cos 255° = (−(√6 + √2)/4) / (−(√6 − √2)/4) = 2 + √3

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

xyOP

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

T(1, tan 255°) ≈ (1, 3.7321) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed); T is beyond the drawing, the arrow points to it.

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: tan 75° = 2 + √3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
234°√(25 + 10√5)/5
240°√3
252°√(5 + 2√5)
255°2 + √3
270°undefined
285°−2 − √3
288°−√(5 + 2√5)

FAQ

What is tan 255°?

tan 255° = 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 0.5873 for tan 255?

The calculator is in radian mode (RAD): it takes tan 255 as the tangent of 255 radians, tan 255 rad ≈ 0.5873. Switch it to degrees (DEG): tan 255° = 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