Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.