Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises - Page 38: 72

$-0.75$

$\sin^{2}\theta+\cos^{2}\theta=1$ $\implies (0.6)^{2}+\cos^{2}\theta=1$ $\implies \cos^{2}\theta=1-(0.6)^{2}=0.64$ Now, $\tan^{2}\theta=\sec^{2}\theta-1=\frac{1}{\cos^{2}\theta}-1$ $=\frac{1}{0.64}-1=0.5625$ $\tan\theta=\pm \sqrt {0.5625}=\pm 0.75$ $\tan \theta$ is negative in the second quadrant. Therefore, $\tan\theta=-0.75$