Mathematics

Problem

Let

\theta

be an angle such that

\sin\theta=\dfrac{3}{5}

and

\cos\theta<0

. (a) Find the exact value of

\cos\theta

. (b) Hence calculate

\tan\theta

in simplest form. (c) Identify the quadrant in which

\theta

lies. (d) Verify that

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

for the values obtained.