1) In this question, we can notice that theta is in Quadrant IV. In this quadrant, the cosine of theta yields a positive value.
2) So, let's make use of a Pythagorean Identity to find the value of the cosine of theta, given the sine of that same angle:
[tex]\begin{gathered} \sin ^2(\theta)+\cos ^2(\theta)=1 \\ (-\frac{3}{5})^2+\cos ^2(\theta)=1 \\ \frac{9}{25}+\cos ^2(\theta)=1 \\ \cos ^2(\theta)=1-\frac{9}{25} \\ \cos ^2(\theta)=\frac{25}{25}-\frac{9}{25} \\ \cos ^2(\theta)=\frac{16}{25} \\ \sqrt[]{\cos ^2(\theta)}=\sqrt[]{\frac{16}{25}} \\ \cos (\theta)=\frac{4}{5} \end{gathered}[/tex]3) Thus the cosine of theta is 4/5 for in Quadrant IV cosine is positive.