The question is shown below.

Question

At an amusement park, the pendulum ride's movement from its starting position in meters can be represented by the equation  If x represents time measured in seconds since the ride first began, at what times will the pendulum's movement be 4 meters from its starting position?

Answer 1

-2cos(x/4) +2

the pendulem is 4 meters high when

-2co(x/4) +2 = 4

then cos(x/4) = -1

x/4 = pi

x = 4pi seconds= about 12.57 seconds

= about 13 seconds

or

the starting position is when t=0 and

-2cos(0/4) +2 = -2cos0 +2

= -2+2 = 0

4 meters from the starting position is

the maximum height, when -2cos(x/4) +2 = 4

-2cos(x/4) = 2

cos(x/4) =-1

x/4 = pi

x = 4pi = about 13 seconds

UNLESS, by chance, you really meant

-2cos(x/4 +2)= -2cos(1/4)(x +8)

then

it never reaches 4 meters high, as 2 meters is the max height

the starting position is when -2cos(0/4 +2) = -2cos2

which can't = more than 2, regardless whether 2 means 2 degrees or 2 radians

Answer 2

Given that f(x) is the distance from the starting position and x is the time in seconds, we can set f(x)=4 meters and solve for x.

Step 1

4 = -2*cos(x/4)+2

Step 2: Subtract 2 from each side

2=-2*cos(x/4)

Step 3: Divide -2 from each side

-1=cos(x/4)

Step 4: Take the inverse cosine of each side

arccos(-1)=arccos(cos(x/4)

Step 5: Solve

pi = x/4

Step 6: Multiply 4 to each side to isolate the variable

4*pi=4(x/4)

Step 7: Solve

4pi = x

This means that every 4pi seconds (or about 12 seconds) the pendulum ride will be 4 meters from its starting position