Tan(270°) = undefined
Tangent — sine divided by cosine, equivalently opposite/adjacent in a right triangle; undefined where cos = 0.
How to derive tan(270°)
tan(270°) = sin(270°)/cos(270°) = (−1)/0, again undefined. The terminal side is vertical (pointing down), and the slope of a vertical line is not defined. Like 90°, the function has a vertical asymptote here.
Unit-circle context
The angle 270° corresponds to 3π/2 radians and sits on an axis on the unit circle.
Its reference angle is 90°, which is why tan(270°) shares its absolute value with tan(90°).
Other trig values at 270°
Related tan values
Frequently asked
- What is the exact value of tan(270°)?
- The exact value is undefined. It does not have a finite decimal value — it is undefined.
- How do you derive tan(270°)?
- tan(270°) = sin(270°)/cos(270°) = (−1)/0, again undefined. The terminal side is vertical (pointing down), and the slope of a vertical line is not defined. Like 90°, the function has a vertical asymptote here.
- What is 270° in radians?
- 270° equals 3π/2 radians (multiply degrees by π/180).
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