Mathematics

Problem

The point

R\bigl(-\tfrac{7}{25},\,\tfrac{24}{25}\bigr)

on the unit circle corresponds to the angle

2\theta

, where

90^{\circ}<2\theta<180^{\circ}

. a. (i) Write down the values of

\sin2\theta

\cos2\theta

and

\tan2\theta

. b. (ii) Using suitable trigonometric identities, form simultaneous equations in

\sin\theta

and

\cos\theta

and solve them to obtain their exact values. c. (iii) State the quadrant in which

\theta

lies, giving reasons based on your answers in part (ii). d. (iv) Calculate

\tan\theta

and verify that

1+\tan^{2}\theta=\sec^{2}\theta

for this angle.