if csc theta = a/b
what are the other five trigonometric angles for theta?
If you have a right angled triangle, with adjacent(perpendicular) = p, hypotenuse = h, and base = b, then with respect to angle $\displaystyle \theta$, the trigonometric functions are defined as:
$\displaystyle sin\theta = \frac{p}{h}$
likewise,
$\displaystyle csc\theta = \frac{1}{sin\theta}=\frac{h}{p}$
you have $\displaystyle \frac{h}{p} = \frac{a}{b}$
use Pythagorean Theorem to find the base (b), and calculate the remaining trigonometric functions.
This link might be helpful:
Trigonometric functions - Wikipedia, the free encyclopedia
Your question has:
$\displaystyle csc\theta = \frac{a}{b}$
that is:
$\displaystyle \frac{\text{hypotenuse}}{\text{adjacent}} = \frac{a}{b}$
By pythagoras theorem:
$\displaystyle {\text{hypotenuse}^2} = {\text{adjacent}^2}+{\text{base}^2}$
so,
$\displaystyle a^2 = b^2 + x^2$ where x is the base
now find he value of x from this equation. Then you will have the values of hypotenuse, adjacent, and base. Then find the trigonometric functions from the link that I provided in the above post!