What is the value of csc (tan^-1 square root 3/3)

Question

Csc(tan^-1 √3/3)

Answer 1

Let θ = Tan^-1(√3/3) = Tan^-1(1/√3)

 

Draw a right triangle with acute angle θ.  label the side opposite θ as 1 and the side adjacent θ as √3.  By the Pythagorean Theorem, the hypotenuse is 2. 

 

So, csc(Tan^-1(1/√3) = cscθ = hypotenuse/opposite = 2/1 = 2.