Tan 570 Degrees: Tangent of 570° on the Unit Circle

What is tan 570°?

Answer

tan 570° =

√3/3 ≈ 0.5774

Angle in radians: 570° = 19π/6. 570° = 360° + 210° — a full turn plus 210°, quadrant III, where tangent is positive.

≈ — rounded to 4 decimal places.

tan 570° = tan(570° − 360°) = tan 210°

tan 210° = tan(180° + 30°) = tan 30° = √3/3

tan 570° = sin 570° / cos 570° = (−1/2) / (−√3/2) = √3/3

Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

tan 30° = (1/2) / (√3/2) = 1/√3 = √3/3

P(cos 570°, sin 570°) ≈ (−0.8660, −0.5)

T(1, tan 570°) ≈ (1, 0.5774) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

+1 turn: the drawing shows 210°.

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