Tan 306 Degrees
Sin, Cos, Tan, Cot of an Angle
What is tan 306°?
Answer
tan 306° =
−√(25 + 10√5)/5 ≈ −1.3764
Angle in radians: 306° = 17π/10. The point of the angle is in quadrant IV, where tangent is negative.
≈ — rounded to 4 decimal places.
tan 306° = tan(360° − 54°) = −tan 54° = −√(25 + 10√5)/5
tan 306° = sin 306° / cos 306° = (−(√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
P(cos 306°, sin 306°) ≈ (0.5878, −0.8090)
T(1, tan 306°) ≈ (1, −1.3764) — where line OP meets the line x = 1.
| Function | Exact value | Decimal |
|---|---|---|
| sin 306° | −(√5 + 1)/4 | ≈ −0.8090 |
| cos 306° | √(10 − 2√5)/4 | ≈ 0.5878 |
| tan 306° | −√(25 + 10√5)/5 | ≈ −1.3764 |
| cot 306° | −√(5 − 2√5) | ≈ −0.7265 |
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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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