Verified Answer :

mathdragon

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

The solutions to the trigonometric equation are given by:

\(x = \frac{\pi}{18}, \frac{7\pi}{18}\)

What is the trigonometric equation?

The trigonometric equation is given by:

\(\cot{(3x)} = \sqrt{3}\)

The cotangent is given by cosine divided by sine, and is \(\sqrt{3}\) for \(\frac{\pi}{6}\), on the first quadrant, and for \(\frac{7\pi}{6}\), on the third quadrant, hence:

\(\cot{(3x)} = \cot{\left(\frac{\pi}{6}\right)}\)

\(3x = \frac{\pi}{6}\)

\(x = \frac{\pi}{18}\)

\(\cot{(3x)} = \cot{\left(\frac{7\pi}{6}\right)}\)

\(3x = \frac{7\pi}{6}\)

\(x = \frac{7\pi}{18}\)

Hence the solutions are:

\(x = \frac{\pi}{18}, \frac{7\pi}{18}\)

More can be learned about trigonometric equations at https://brainly.com/question/24680641

Related Questions