Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Answer:
[tex]\frac{63}{65}[/tex]
Step-by-step explanation:
The angle theta terminates in quadrant 4, so we know [tex]\frac{3\pi}{2} < \theta < 2\pi[/tex] and that the sin is negative and the cos is positive.
Using the Pythagorean identity [tex]\sin^2\theta+\cos^2\theta=1[/tex], we substitute [tex]\sin\theta[/tex] to find [tex]\cos\theta[/tex] :
[tex](-\frac{16}{65})^2+\cos^2\theta=1[/tex].
Solving for [tex]\cos\theta[/tex], we have
[tex]\cos^2\theta=1-\frac{256}{4225}\\[/tex],
[tex]\cos^2\theta=\frac{3969}{4225}[/tex].
Taking the square root of both sides gives
[tex]\cos\theta=\pm\frac{63}{65}[/tex].
We found before that since the angle theta terminates in quadrant 4, the cos is positive, so we take the positive square root to get
[tex]\cos\theta=\frac{63}{65}[/tex].
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
