Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Find the values of cosΘ and tanΘ, given that sinΘ = 8/9 and Θ is in quadrant I

Sagot :

kate200468
[tex]sin^2 \alpha +cos^2 \alpha =1\ \ \ and\ \ \ tan \alpha = \frac{\big{sin \alpha }}{\big{cos \alpha }} \\\\sin \alpha = \frac{8}{9}\\\\ \Rightarrow\ \ \ (\frac{8}{9})^2+cos^2 \alpha =1\ \ \ \Rightarrow\ \ \ cos^2 \alpha =1- \frac{64}{81} \ \ \ \Rightarrow\ \ \ cos^2 \alpha = \frac{17}{81} \\\\ \alpha \ \in\ (0^0;90^0)\ \ \ \Rightarrow\ \ \ cos \alpha >0\ \ \ \Rightarrow\ \ \ cos \alpha = \frac{ \sqrt{17} }{9} \\\\[/tex]

[tex]tan \alpha = \frac{8}{9}: \frac{ \sqrt{17} }{9} =\frac{8}{9}\cdot \frac{9}{\sqrt{17}}= \frac{8}{\sqrt{17}}= \frac{8\cdot \sqrt{17}}{\sqrt{17}\cdot \sqrt{17}}=\frac{8\cdot \sqrt{17}}{17}[/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.