Respuesta :

bantheundead

Answer: the solutions are therefore 45 105 165 225 285 345

Step-by-step explanation:

Divide both sides by 4 to get

\tan(3x)=-1

Recalling the definition of tangent as ratio between sine and cosine, we have

\tan(3x)=-1 \iff \dfrac{\sin(3x)}{\cos(3x)}=-1 \iff \sin(3x)=-\cos(3x)

The sine and cosine of an angle are opposite only if the angle is

\alpha = 135+180k,\quad k \in \mathbb{Z}

So, we have

3x=135+180k \iff x = 45+60k,\quad k \in \mathbb{Z}

So, the solutions are

tramserran

Answer:  c) 45°, 105°, 165°, 225°, 285°, 345°

Step-by-step explanation:

4 tan (3x) = -4

  tan (3x) = -1

tan⁻¹ [tan (3x)] = tan⁻¹ (-1)

Where on the Unit Circle does sin/cos = -1  →  at  135°  and  315°

All possible solutions are: 135° + 360n   and     315° + 360n

:n = number of rotations

3x = 135    -->    x = 45

3x = 315   -->     x = 105

3x = 135 + 360     -->   3x = 495    -->  x = 165

3x = 315 + 360    -->    3x = 675    -->  x = 225

3x = 135 + 360(2)   --->   3x =  855   ---> x = 285

3x = 315 + 360(2)   --->   3x = 1035   ---> x = 345

Note that n = 3 results in x > 360 so these are the only valid solutions

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