Question

Solve for x

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

Worth 6 marks

Answer 1

Answer: x = 115.5°

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°