A tire swing is suspended from a tree. The swings height (in feet) above the ground is modeled by the equation, h = -12cos(x) + 15. (x is the angle measured in degrees). What is the height of the swing, when the angle is 60 degrees?
cos 60 = 1/2
h = -12(1/2) + 15
h = -6 + 15
h = 11
To find the height of the swing when the angle is 60 degrees, we need to substitute x = 60 degrees into the equation h = -12cos(x) + 15.
First, let's convert 60 degrees to radians since the cosine function takes input in radians. To convert degrees to radians, we multiply the degree measure by π/180.
60 degrees * π/180 = π/3 radians
Now, substitute x = π/3 into the equation:
h = -12cos(π/3) + 15
Next, evaluate cos(π/3). The cosine of π/3 is equal to 1/2.
So, h = -12 * (1/2) + 15
Now, simplify the equation:
h = -6 + 15
h = 9
Therefore, when the angle is 60 degrees, the height of the swing is 9 feet above the ground.