Tan(15°) = 2 − √3
Tangent — sine divided by cosine, equivalently opposite/adjacent in a right triangle; undefined where cos = 0.
How to derive tan(15°)
tan(15°) = sin(15°)/cos(15°) = ((√6 − √2)/4) / ((√6 + √2)/4) = (√6 − √2)/(√6 + √2). Rationalising the denominator gives 2 − √3.
Unit-circle context
The angle 15° corresponds to π/12 radians and sits Quadrant I on the unit circle.
Other trig values at 15°
Related tan values
Frequently asked
- What is the exact value of tan(15°)?
- The exact value is 2 − √3. Its decimal approximation is 0.26795.
- How do you derive tan(15°)?
- tan(15°) = sin(15°)/cos(15°) = ((√6 − √2)/4) / ((√6 + √2)/4) = (√6 − √2)/(√6 + √2). Rationalising the denominator gives 2 − √3.
- What is 15° in radians?
- 15° equals π/12 radians (multiply degrees by π/180).
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