Tan 252 Degrees
Sin, Cos, Tan, Cot of an Angle
What is tan 252°?
Answer
tan 252° =
√(5 + 2√5) ≈ 3.0777
Angle in radians: 252° = 7π/5. The point of the angle is in quadrant III, where tangent is positive.
≈ — rounded to 4 decimal places.
tan 252° = tan(180° + 72°) = tan 72° = √(5 + 2√5)
tan 252° = sin 252° / cos 252° = (−√(10 + 2√5)/4) / (−(√5 − 1)/4) = √(5 + 2√5)
Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.
tan 72° = cot 18° = cos 18° / sin 18° = √(5 + 2√5)
P(cos 252°, sin 252°) ≈ (−0.3090, −0.9511)
T(1, tan 252°) ≈ (1, 3.0777) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed); T is beyond the drawing, the arrow points to it.
| Function | Exact value | Decimal |
|---|---|---|
| sin 252° | −√(10 + 2√5)/4 | ≈ −0.9511 |
| cos 252° | −(√5 − 1)/4 | ≈ −0.3090 |
| tan 252° | √(5 + 2√5) | ≈ 3.0777 |
| cot 252° | √(25 − 10√5)/5 | ≈ 0.3249 |
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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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