Answer :
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
