Respuesta :

tonb
cos x = 1 for any multiple of 360°

So cos 3x is 1 for any multiple of 120°

In the interval 0° < x < 180°, only x=120° is a valid solution (not x=0°!!)

The solution is x = 120º

This question is the solution of a trigonometric equation, involving cosine.

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Standard equation:

[tex]\cos{(ax)} = 1[/tex] has the solutions given by:

[tex]x = \frac{2n\pi}{a}[/tex]

In which n = 0, 1, 2,...

Considering that [tex]2\pi = 360[/tex], the solution, in degrees, is:

[tex]x = \frac{360n}{a}[/tex]

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In this question:

[tex]\cos{(3x)} = 1[/tex]

Thus, a = 3, and the solution is:

[tex]x = \frac{360n}{3} = 120n[/tex]

  • n = 0: x = 120(0) = 0º
  • n = 1: x = 120(1) = 120º
  • n = 2: x = 120(2) = 240º
  • ....

We want solutions greater than 0º and less than 180º, so the solution is x = 120º.

A similar example is found at https://brainly.com/question/16756406

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