Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.7 Derivatives And Integrals Involving Inverse Trigonometric Functions - Exercises Set 6.7 - Page 469: 1

$${\text{sin}}\theta = \frac{4}{5},{\text{ }}\cos \theta = \frac{3}{5},{\text{ }}\sec \theta = \frac{5}{3},{\text{ }}\csc \theta = \frac{5}{4}$$

$$\eqalign{ & \theta = {\tan ^{ - 1}}\left( {\frac{4}{3}} \right) \cr & {\text{From the triangle shown below,}} \cr & \tan \theta = \frac{4}{3} \Rightarrow \theta = {\tan ^{ - 1}}\left( {\frac{4}{3}} \right) \cr & {\text{Therefore,}} \cr & {\text{sin}}\theta = \frac{4}{5} \cr & \cos \theta = \frac{3}{5} \cr & \sec \theta = \frac{1}{{\sin \theta }} = \frac{5}{3} \cr & \csc \theta = \frac{1}{{\cos \theta }} = \frac{5}{4} \cr} $$