What is the cosecant of Angle C?

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Question:

What is the cosecant of Angle C?

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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:[tex]c^2 = a^2+b^2[/tex][tex]c = \sqrt{a^2+b^2} [/tex][tex]c = \sqrt{(-8)^2+(-6)^2} = \sqrt{100} = 10[/tex]Now, we can solve for cosine:[tex]cos(C) = \frac{BC}{AC} = -\frac{6}{10} = - \frac{3}{5} [/tex]Cosecant is the reciprocal of that, so your answer is:[tex]csc(C) = -\frac{5}{3} [/tex]Hope this helps! 

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