Tan 15 Degrees

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

What is tan 15°?

Answer

tan 15° =
2 − √3 ≈ 0.2679

Angle in radians: 15° = π/12. The point of the angle is in quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places.

tan 15° = sin 15° / cos 15° = ((√6 − √2)/4) / ((√6 + √2)/4) = 2 − √3

tan 15° = tan(45° − 30°) = (1 − √3/3) / (1 + √3/3) = 2 − √3

xyOP

P(cos 15°, sin 15°) ≈ (0.9659, 0.2588)

T(1, tan 15°) ≈ (1, 0.2679) — where line OP meets the line x = 1.

All four functions of 15°
FunctionExact valueDecimal
sin 15°(√6 − √2)/4≈ 0.2588
cos 15°(√6 + √2)/4≈ 0.9659
tan 15°2 − √3≈ 0.2679
cot 15°2 + √3≈ 3.7321

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
12°≈ 0.2126
13°≈ 0.2309
14°≈ 0.2493
15°2 − √3
16°≈ 0.2867
17°≈ 0.3057
18°√(25 − 10√5)/5

FAQ

What is tan 15°?

tan 15° = 2 − √3 ≈ 0.2679

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 −0.8560 for tan 15?

The calculator is in radian mode (RAD): it takes tan 15 as the tangent of 15 radians, tan 15 rad ≈ −0.8560. Switch it to degrees (DEG): tan 15° = 2 − √3 ≈ 0.2679. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also