Tan 126 Degrees

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

What is tan 126°?

Answer

tan 126° =
−√(25 + 10√5)/5 ≈ −1.3764

Angle in radians: 126° = 7π/10. The point of the angle is in quadrant II, where tangent is negative.

≈ — rounded to 4 decimal places.

tan 126° = tan(180° − 54°) = −tan 54° = −√(25 + 10√5)/5

tan 126° = sin 126° / cos 126° = ((√5 + 1)/4) / (−√(10 − 2√5)/4) = −√(25 + 10√5)/5

Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

tan 54° = cot 36° = cos 36° / sin 36° = √(25 + 10√5)/5

xyOP

P(cos 126°, sin 126°) ≈ (−0.5878, 0.8090)

T(1, tan 126°) ≈ (1, −1.3764) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 126°
FunctionExact valueDecimal
sin 126°(√5 + 1)/4≈ 0.8090
cos 126°−√(10 − 2√5)/4≈ −0.5878
tan 126°−√(25 + 10√5)/5≈ −1.3764
cot 126°−√(5 − 2√5)≈ −0.7265

Reference angle: tan 54° = √(25 + 10√5)/5

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
110°≈ −2.7475
120°−√3
125°≈ −1.4281
126°−√(25 + 10√5)/5
127°≈ −1.3270
130°≈ −1.1918
134°≈ −1.0355

FAQ

What is tan 126°?

tan 126° = −√(25 + 10√5)/5 ≈ −1.3764

How are sin 36° and cos 54° related?

They are equal: sin α = cos(90° − α), and 36° + 54° = 90°. So sin 36° = cos 54° = √(10 − 2√5)/4, cos 36° = sin 54° = (√5 + 1)/4, and tan 36° = cot 54° = √(5 − 2√5).

Why does a calculator show 0.3496 for tan 126?

The calculator is in radian mode (RAD): it takes tan 126 as the tangent of 126 radians, tan 126 rad ≈ 0.3496. Switch it to degrees (DEG): tan 126° = −√(25 + 10√5)/5 ≈ −1.3764. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also