Calculate the tangent of an angle in degrees or radians with undefined-angle detection at 90 and 270 degrees.
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Trigonometry
The tangent calculator computes the tangent of any angle in degrees or radians. It detects undefined values at 90°, 270°, and other odd multiples of 90° where the tangent approaches infinity.
Tangent is the ratio of sine to cosine: tan(θ) = sin(θ) / cos(θ). In a right triangle, it equals the opposite side divided by the adjacent side.
Tangent is undefined wherever cosine equals zero — at 90°, 270°, and all angles of the form (2k+1) × 90°. At these points, the function approaches positive or negative infinity.
Common exact values: tan(0°) = 0, tan(30°) = root3/3, tan(45°) = 1, tan(60°) = root3. The tangent function has period 180° (pi radians).
Frequently asked questions
Because cos(90°) = 0 and tangent is sin/cos. Division by zero is undefined. Graphically, the tangent curve has a vertical asymptote at 90°.
Exactly 1. In a 45-45-90 triangle, the two legs are equal, so opposite/adjacent = 1.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Calculate the arctangent (inverse tangent) of any real number and return the angle in degrees and radians.
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Calculate the arcsine (inverse sine) of a value and return the angle in degrees and radians with exact fractions of pi.
Calculate the sine of an angle in degrees or radians with exact values for common angles like 30, 45, and 60 degrees.
