Mathematics

Problem

For an angle

x

, it is known that

\cot x>0

and

\sec x<0

. a. (i) Determine all possible quadrants in which the terminal side of

x

can lie. Justify your answer using the signs of the trigonometric ratios. b. (ii) If, in addition,

\tan x=\dfrac{7}{24}

and

x

satisfies the conditions from part (i), calculate

\sin x

and

\cos x

. c. (iii) Using the results of part (ii), obtain

\sin 2x

and

\cos 2x

in simplest form.