Question

What is the cosecant of Angle C?

Answer 1

Cosecant is a trigonometric ratio that is the reciprocal of cosine. So, we can just figure out the cosine of the angle and reciprocal that to find the answer.

Cosine is adjacent/hypotenuse. The hypotenuse of the triangle is AC, and the side adjacent to angle C is CB. First, we need to find the length AC by the Pythagorean Theorem:
$c^2 = a^2+b^2$
$c = \sqrt{a^2+b^2}$
$c = \sqrt{(-8)^2+(-6)^2} = \sqrt{100} = 10$

Now, we can solve for cosine:
$cos(C) = \frac{BC}{AC} = -\frac{6}{10} = - \frac{3}{5}$

Cosecant is the reciprocal of that, so your answer is:
$csc(C) = -\frac{5}{3}$

Hope this helps!