Tan(75°) = 2 + √3
Tangent — sine divided by cosine, equivalently opposite/adjacent in a right triangle; undefined where cos = 0.
How to derive tan(75°)
tan(75°) = sin(75°)/cos(75°) = ((√6 + √2)/4) / ((√6 − √2)/4) = (√6 + √2)/(√6 − √2). Rationalising the denominator gives 2 + √3.
Unit-circle context
The angle 75° corresponds to 5π/12 radians and sits Quadrant I on the unit circle.
Other trig values at 75°
Related tan values
Frequently asked
- What is the exact value of tan(75°)?
- The exact value is 2 + √3. Its decimal approximation is 3.73205.
- How do you derive tan(75°)?
- tan(75°) = sin(75°)/cos(75°) = ((√6 + √2)/4) / ((√6 − √2)/4) = (√6 + √2)/(√6 − √2). Rationalising the denominator gives 2 + √3.
- What is 75° in radians?
- 75° equals 5π/12 radians (multiply degrees by π/180).
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