jake4157 jake4157
  • 13-06-2022
  • Mathematics
contestada

Solve 3cot (2x) =- Route3 for
x, 0 = x < 360

Respuesta :

culveryolanda46
culveryolanda46 culveryolanda46
  • 13-06-2022

Answer:

x=60,150,240,330

Step-by-step explanation:

[tex]3 \cot(2x) = - \sqrt{3} [/tex]

[tex] \cot(2x) = \frac{ - \sqrt{3} }{3} [/tex]

Take the arc cot of both sides

[tex] \cot {}^{ - 1} ( \cot(2x) ) = \cot {}^{ - 1} ( \frac{ - \sqrt{3} }{3} ) [/tex]

[tex]2x = 120[/tex]

Remember cotangent has a period of 180 degrees

[tex]2x = 120 + 90(n)[/tex]

where n is 0, 1,2,3,4,5.....

Isolate x.

[tex]x = 60 + 90(n)[/tex]

where n is 0, 1,2,3,4,5,6.

Keep plugging in integers as long they are in the interval [0,360].

We get

60,150,240,330.

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