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If θ is an angle in standard position and its terminal side passes through the point (1,-8), find the exact value of csc θ in simplest radical form.

Sagot :

Check the picture below.

well, we know the angle's cosine and sine or namely adjacent and opposite sides, let's get the hypotenuse.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{1}\\ b=\stackrel{opposite}{-8}\\ \end{cases} c=\sqrt{1^2+(-8)^2}\implies c=\sqrt{65} \\\\[-0.35em] ~\dotfill\\\\ csc(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{65}}}{\underset{opposite}{-8}}\implies csc(\theta )=-\cfrac{\sqrt{65}}{8}[/tex]

View image jdoe0001
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