Question

Cos(x/6+3)=1

Answer 1

cos(x/6+3)=1

x/6+3=2*pi*n

x/6=2*pi*n-3

x=12*pi*n-18

 

Answer 2

To solve for x in the equation cos(x/6+3) = 1, we can start by using the definition of cosine:

cosine(angle) = adjacent side / hypotenuse

We can rewrite the given equation as:

cos(x/6+3) = cos(0)

Since the cosine function has a period of 2π, we can add or subtract multiples of 2π to the angle inside the cosine function without changing its value. Therefore, we can write:

x/6 + 3 = 2πn or x/6 + 3 = 2πn + 2π

where n is any integer.

Solving for x in the first equation, we get:

x/6 = 2πn - 3

x = 12πn - 18

Solving for x in the second equation, we get:

x/6 = 2πn - 3 - 2π

x = 12πn - 30

So the solutions for x are:

x = 12πn - 18 or x = 12πn - 30

where n is any integer.