Tan 216 Degrees
Sin, Cos, Tan, Cot of an Angle
What is tan 216°?
Answer
tan 216° =
√(5 − 2√5) ≈ 0.7265
Angle in radians: 216° = 6π/5. The point of the angle is in quadrant III, where tangent is positive.
≈ — rounded to 4 decimal places.
tan 216° = tan(180° + 36°) = tan 36° = √(5 − 2√5)
tan 216° = sin 216° / cos 216° = (−√(10 − 2√5)/4) / (−(√5 + 1)/4) = √(5 − 2√5)
Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.
tan 36° = sin 36° / cos 36° = √(5 − 2√5)
P(cos 216°, sin 216°) ≈ (−0.8090, −0.5878)
T(1, tan 216°) ≈ (1, 0.7265) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).
| Function | Exact value | Decimal |
|---|---|---|
| sin 216° | −√(10 − 2√5)/4 | ≈ −0.5878 |
| cos 216° | −(√5 + 1)/4 | ≈ −0.8090 |
| tan 216° | √(5 − 2√5) | ≈ 0.7265 |
| cot 216° | √(25 + 10√5)/5 | ≈ 1.3764 |
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See Also
- Arcsin, Arccos, Arctan, Arccot - The angle from the value of its sine, cosine, tangent or cotangent: exact in degrees and π, with the check and the unit circle
- Square Root Calculator - Calculate the square root of any number
- Simplify Square Root Calculator - Write any square root in simplest radical form, step by step
- Geometry Formulas: Area, Volume, Perimeter - The formula for every standard shape, where it comes from, and worked examples
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