Tan 234 Degrees

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

What is tan 234°?

Answer

tan 234° =
√(25 + 10√5)/5 ≈ 1.3764

Angle in radians: 234° = 13π/10. The point of the angle is in quadrant III, where tangent is positive.

≈ — rounded to 4 decimal places.

tan 234° = tan(180° + 54°) = tan 54° = √(25 + 10√5)/5

tan 234° = sin 234° / cos 234° = (−(√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 234°, sin 234°) ≈ (−0.5878, −0.8090)

T(1, tan 234°) ≈ (1, 1.3764) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 234°
FunctionExact valueDecimal
sin 234°−(√5 + 1)/4≈ −0.8090
cos 234°−√(10 − 2√5)/4≈ −0.5878
tan 234°√(25 + 10√5)/5≈ 1.3764
cot 234°√(5 − 2√5)≈ 0.7265

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

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
216°√(5 − 2√5)
225°1
227°≈ 1.0724
234°√(25 + 10√5)/5
240°√3
252°√(5 + 2√5)
255°2 + √3

FAQ

What is tan 234°?

tan 234° = √(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 20.5376 for tan 234?

The calculator is in radian mode (RAD): it takes tan 234 as the tangent of 234 radians, tan 234 rad ≈ 20.5376. Switch it to degrees (DEG): tan 234° = √(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