Tan 450 Degrees: Tangent of 450° on the Unit Circle

What is tan 450°?

Answer

tan 450°

is undefined

Angle in radians: 450° = 5π/2. 450° = 360° + 90° — a full turn plus 90°: the point is on the y-axis, (0, 1).

cos 450° = 0, and tan = sin / cos: you can't divide by zero, so the value doesn't exist.

tan 450° = tan(450° − 360°) = tan 90°

tan 450° = sin 450° / cos 450° = 1 / 0

P(cos 450°, sin 450°) = (0, 1)

Line OP of 450° runs parallel to the line x = 1: they never meet, so tan 450° doesn't exist.

+1 turn: the drawing shows 90°.

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