Answered

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Solve the following equation on the interval [0,2 \pi)
Cot(3x)=\sqrt{3}

Sagot :

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:

[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

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