Tangent Calculator

tan(x) = sin(x) / cos(x). Undefined where cos(x) = 0 (at 90°, 270°, …).

Inputs

Result

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How to use this calculator

  • Enter the angle.
  • Read tan; the breakdown shows sin and cos used in the calculation.

About this calculator

tan(x) = sin(x) / cos(x). On the unit circle, tan is the slope of the radius. Period π (not 2π). Vertical asymptotes where cos = 0 (at 90°, 270°, etc.). tan(45°) = 1; tan(0°) = 0.

Frequently asked

Why is tan(90°) undefined?+
cos(90°) = 0, and division by zero is undefined. tan has a vertical asymptote there.
What's the period of tan?+
π radians (180°), not 2π. tan(x + 180°) = tan(x).
Where is tan(45°) = 1?+
Because sin(45°) = cos(45°) = √2/2, so their ratio is 1.
Can tan be negative?+
Yes — in quadrants II and IV (90°-180° and 270°-360°), where sin and cos have opposite signs.
How does tan relate to slope?+
tan of the angle a line makes with the x-axis equals the line's slope. tan(45°) = 1 means a 45° line has slope 1.

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