Given #theta = (19pi) / 6# how do you find #tantheta#? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Alan P. Jun 30, 2015 #tan((19pi)/6) = 1/sqrt(3)# Explanation: #theta =(19 pi)/6 = 2pi + (pi+pi/6)# So #theta# has a reference angle of #pi/6# in quadrant 3. #tan(theta)# is positive in quadrant 3 and #pi/6# is a standard angle with #tan(pi/6) = 1/sqrt(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 5253 views around the world You can reuse this answer Creative Commons License