Answer
$sin \phi=\frac{\sqrt 5}{3}$
$cos \phi=-\frac{2}{3}$
$tan \phi=-\frac{\sqrt 5}{2}$
$csc \phi=\frac{3\sqrt 5}{5}$
$cot \phi=-\frac{2\sqrt 5}{5}$
Work Step by Step
Since $sec \phi=-1.5=-\frac{3}{2}$, we can label the hypotenuse side as having length 3 and the adjacent side as having length 2.
Then Pythagorean Theorem gives
opposite side $=\sqrt {3^{2}-2^{2}}=\sqrt 5$
As $\frac{\pi}{2}0,cos\phi<0,tan\phi<0$
The other five trigonometric functions are given as follows:
$sin \phi=\frac{\sqrt 5}{3}$
$cos \phi=-\frac{2}{3}$
$tan \phi=-\frac{\sqrt 5}{2}$
$csc \phi=\frac{3\sqrt 5}{5}$
$cot \phi=-\frac{2\sqrt 5}{5}$
