I. Since [tex]\theta[/tex] lies in quadrant 3, we know [tex]\cos\theta<0[/tex]. The Pythagorean identity tells us
[tex]\cos^2\theta+\sin^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=\boxed{-\dfrac45}[/tex]
[tex]\implies\sec\theta=\dfrac1{\cos\theta}=\boxed{-\dfrac54}[/tex]
II. By definition of tangent,
[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{-\frac35}{-\frac45}=\boxed{\dfrac34}[/tex]
