Mathematics

Problem

In a right-angled triangle

\triangle ABC

, right angled at

C

, the measure of the acute angle

A

satisfies

\sin A = \dfrac{3}{5}

. Use this information to answer the following. a. (i) Find the values of

\cos(90^{\circ}-A)

and

\sec(90^{\circ}-A)

. b. (ii) Evaluate

P = \sin A + \cos(90^{\circ}-A) + \tan(90^{\circ}-A)

and give your answer as a rational number. c. (iii) Using the same angle

A

, compute

Q = \sin A\,\csc(90^{\circ}-A) + \cos A\,\sec(90^{\circ}-A)

and express your answer in simplest form.