Use the following identities:
[tex]sec^2 = 1 + tan^2 \\ \\ sec = \frac{1}{cos} \\ \\ sin^2 = 1 - cos^2[/tex]
Also because the angle is in quadrant 3, sin must be negative.
Therefore
[tex]sin = - \sqrt{1 - \frac{1}{1 + tan^2}}[/tex]
Subbing in tan = 0.958
[tex]sin \theta = -0.69178[/tex]
