Tan(105°) = −(2 + √3)
Tangent — sine divided by cosine, equivalently opposite/adjacent in a right triangle; undefined where cos = 0.
How to derive tan(105°)
105° is in quadrant II where tangent is negative. Reference angle = 75°, so tan(105°) = −tan(75°) = −(2 + √3).
Unit-circle context
The angle 105° corresponds to 7π/12 radians and sits Quadrant II on the unit circle.
Its reference angle is 75°, which is why tan(105°) shares its absolute value with tan(75°).
Other trig values at 105°
Related tan values
Frequently asked
- What is the exact value of tan(105°)?
- The exact value is −(2 + √3). Its decimal approximation is -3.73205.
- How do you derive tan(105°)?
- 105° is in quadrant II where tangent is negative. Reference angle = 75°, so tan(105°) = −tan(75°) = −(2 + √3).
- What is 105° in radians?
- 105° equals 7π/12 radians (multiply degrees by π/180).
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