Mathematics

Problem

For an angle

\alpha

it is given that

\sin\alpha=-\dfrac{3}{5}

and

\cos\alpha=\dfrac{4}{5}

. Answer the following. a. Verify that

\sin^{2}\alpha+\cos^{2}\alpha=1

for the given values. b. Identify the quadrant in which

\alpha

lies, giving a brief reason based on the signs of the trigonometric ratios. c. Find the exact value of

\tan\alpha

and justify that its sign is consistent with the quadrant obtained in part (ii).