Mathematics

Problem

Answer the following questions related to the equation

\tan \theta = -1

for

0 \le \theta < 2\pi

. a. (i) Explain why

\theta = \dfrac{\pi}{2}

and

\theta = \dfrac{3\pi}{2}

cannot satisfy the given equation. b. (ii) Using the signs of tangent in the four quadrants, identify the quadrants in which the solutions of

\tan \theta = -1

will lie. c. (iii) Determine the exact values of

\theta

in the interval

0 \le \theta < 2\pi

that satisfy

\tan \theta = -1

, and justify your answer.