Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Giải phương trình sau:
sinx=1/2

Sagot :

Happil

Answer:

[tex]x = \frac{\pi}{6} +2\pi k \space , \space \text{for any integer values of } k\\[/tex]

[tex]x = \frac{5\pi}{6} -2\pi k \space , \space \text{for any integer values of } k\\[/tex]

Step-by-step explanation:

Solving with the Periodicity Identity:

[tex]\sin(x)= \frac{1}{2} \\ x = \arcsin(\frac{1}{2}) +2\pi k \\ x = \frac{\pi}{6} +2\pi k[/tex]

Solving with the Symmetry Identity:

[tex]\sin(x) = \frac{1}{2} \\ \sin(\pi -x) = \frac{1}{2} \\ \pi -x = \arcsin(\frac{1}{2}) +2\pi k \\ \pi -x = \frac{\pi}{6} +2\pi k \\ -x = \frac{\pi}{6} +2\pi k -\pi \\ -x = \frac{\pi}{6} - \frac{6\pi}{6} +2\pi k \\ -x = -\frac{5\pi}{6} + 2\pi k \\ x = \frac{5\pi}{6} -2\pi k[/tex]

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.