How do you find the exact value of tan (23pi/6)? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Ratnaker Mehta Mar 13, 2018 -1/sqrt3, or, -sqrt3/3. Explanation: tan(23/6pi)=tan{(24-1)/6pi}=tan{(24/6-1/6)pi}, =tan(4pi-pi/6). Since, (4pi-pi/6) lies in the fourth quadrant, where, tan is -ve, we get, tan(23/6pi)=tan(4pi-pi/6)=-tan(pi/6)=-1/sqrt3, or, -sqrt3/3. Answer link Related questions How do you find the trigonometric functions of any angle? What is the reference angle? How do you use the ordered pairs on a unit circle to evaluate a trigonometric function of any angle? What is the reference angle for 140^\circ? How do you find the value of cot 300^@? What is the value of sin -45^@? How do you find the trigonometric functions of values that are greater than 360^@? How do you use the reference angles to find sin210cos330-tan 135? How do you know if sin 30 = sin 150? How do you show that (costheta)(sectheta) = 1 if theta=pi/4? See all questions in Trigonometric Functions of Any Angle Impact of this question 5315 views around the world You can reuse this answer Creative Commons License