Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
cot(3x)=3^(1/2)
cot(x)= cos(x)/sin(x)
cot(3x)= cos(3x)/sin(3x)
look at a unit circle chart
find a value for cos that has sqrt(3) in it
which one will reduce so that the cos/sin will equal sqrt(3)?
pi/6 radians
now cot(3x) implies that x is one third this value
pi/18 is the answer
cot(x)= cos(x)/sin(x)
cot(3x)= cos(3x)/sin(3x)
look at a unit circle chart
find a value for cos that has sqrt(3) in it
which one will reduce so that the cos/sin will equal sqrt(3)?
pi/6 radians
now cot(3x) implies that x is one third this value
pi/18 is the answer
The solutions to the trigonometric equation are given by:
[tex]x = \frac{\pi}{18}, \frac{7\pi}{18}[/tex]
What is the trigonometric equation?
The trigonometric equation is given by:
[tex]\cot{(3x)} = \sqrt{3}[/tex]
The cotangent is given by cosine divided by sine, and is [tex]\sqrt{3}[/tex] for [tex]\frac{\pi}{6}[/tex], on the first quadrant, and for [tex]\frac{7\pi}{6}[/tex], on the third quadrant, hence:
[tex]\cot{(3x)} = \cot{\left(\frac{\pi}{6}\right)}[/tex]
[tex]3x = \frac{\pi}{6}[/tex]
[tex]x = \frac{\pi}{18}[/tex]
[tex]\cot{(3x)} = \cot{\left(\frac{7\pi}{6}\right)}[/tex]
[tex]3x = \frac{7\pi}{6}[/tex]
[tex]x = \frac{7\pi}{18}[/tex]
Hence the solutions are:
[tex]x = \frac{\pi}{18}, \frac{7\pi}{18}[/tex]
More can be learned about trigonometric equations at https://brainly.com/question/24680641
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.