Tan(90°) = undefined
Tangent — sine divided by cosine, equivalently opposite/adjacent in a right triangle; undefined where cos = 0.
How to derive tan(90°)
tan(90°) = sin(90°)/cos(90°) = 1/0, which is undefined — division by zero. Geometrically, the tangent line at 90° is vertical and has no finite slope. As x approaches 90° from below, tan(x) tends to +∞; from above, it tends to −∞.
Unit-circle context
The angle 90° corresponds to π/2 radians and sits on an axis on the unit circle.
Other trig values at 90°
Related tan values
Frequently asked
- What is the exact value of tan(90°)?
- The exact value is undefined. It does not have a finite decimal value — it is undefined.
- How do you derive tan(90°)?
- tan(90°) = sin(90°)/cos(90°) = 1/0, which is undefined — division by zero. Geometrically, the tangent line at 90° is vertical and has no finite slope. As x approaches 90° from below, tan(x) tends to +∞; from above, it tends to −∞.
- What is 90° in radians?
- 90° equals π/2 radians (multiply degrees by π/180).
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