find the exact value of the expression... csc(tan^-1 4/5)

Answer 1

Always start by drawing the right triangle. The tangent is the ratio of the opposite side to the adjacent side of the angle; so the opposite side is 4 and the adjacent side is 5. The hypotenuse is √(4²+5²) = √41. The cosecant is equal to the hypotenuse over the opposite side = (√41)/4