How do you evaluate #csc((-4pi)/3)#? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Somebody N. Nov 12, 2017 #(2sqrt(3))/3# Explanation: #csc(theta)=1/sintheta# #(-4pi)/3=pi-(4pi)/3=pi/3# #sin(pi/3)=sqrt(3)/2# #1/(sin(pi/3))=1/(sqrt(3)/2)=(2sqrt(3))/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 4656 views around the world You can reuse this answer Creative Commons License