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Tan 105 Degrees

tan(105°) = -3.73205081, exactly −(2 + √3).

Answer

tan(105°) = -3.73205081, exactly −(2 + √3). The angle 105° equals 7π/12 radians (105 × π/180).

Exact form: −(2 + √3). Decimal: -3.73205081 (rounded to 8 places).

Where 105° sits on the unit circle

105° lies quadrant II. Remember that tangent is positive in quadrants I and III, and negative in the others, which decides the sign of the answer.

How to calculate tan 105° on a scientific calculator

  1. Set the calculator to DEG (degrees) mode.
  2. Press tan.
  3. Type 105.
  4. Press = to get -3.73205081.

If you get a different number, the calculator is probably in RAD mode. In radians you would enter 7π/12 instead of 105.

Quick results

sin 105°= 0.96592583
cos 105°= -0.25881905
tan 105°= -3.73205081

Tan of common angles

AngleRadiansTan
0°00
30°π/60.57735
45°π/41
60°π/31.732051
90°π/2undefined
120°2π/3-1.732051
135°3π/4-1
150°5π/6-0.57735
180°π0
270°3π/2undefined
360°2π0

Frequently Asked Questions

What is tan 105 degrees?

tan(105°) = -3.73205081, exactly −(2 + √3).

What is tan 105° in radians?

105° = 7π/12 radians, so tan(105°) = tan(7π/12) = -3.73205081.

Why does my calculator show a different answer for tan 105?

It is most likely set to radians. Switch to degree (DEG) mode before entering the angle.

Is tan 105° positive or negative?

Negative.

Is there an online scientific calculator I can use for this?

Yes. Use the calculator on this page, or open the full free Scientific Calculator with memory, history and keyboard support.

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