Mathematics

Problem

Suppose

\alpha

is an angle in the third quadrant with

\cos \alpha = -\dfrac{5}{13}

. a. (i) Determine the exact values of

\sin \alpha

and

\tan \alpha

. b. (ii) Find the exact values of

\sec \alpha

and

\csc \alpha

and also write their decimal approximations correct to two decimal places. c. (iii) List all real numbers

x

in the interval

[-2\pi, 2\pi]

for which

\sec x

is not defined.