brianpathmasri brianpathmasri
  • 12-03-2021
  • Mathematics
contestada

Solve for x

2cos(x + 40 ^ 0) = 1/2 for r 0<= x<=360^

Worth 6 marks

Respuesta :

facundo3141592
facundo3141592 facundo3141592
  • 17-03-2021

Answer: x = 115.5°

Step-by-step explanation:

I suppose that we have the equation:

2*cos(x + 40°) = 1/2 for 0° < x < 360°

Let's solve this.

First, we isolate the cosine function:

cos(x + 40°) = (1/2)/2 = 1/4

cos(x + 40°) = 1/4

Now we can use the Acos(x) function, remember that:

Acos(cos(x)) = x

cos(Acos(x)) = x

Then if we use this function in both sides, we get:

Acos( cos(x + 40°)) = Acos(1/4)

x + 40° = Acos(1/4) = 75.5°

x = 75.5° + 40° = 115.5°

x = 115.5°

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