Answer:
Step-by-step explanation:
To calculate the angle theta in the equation:
0.166 = (1 - cos(theta/2)) / 2
We can start by isolating the term cos(theta/2) on one side of the equation:
1 - cos(theta/2) = 0.166 * 2
1 - cos(theta/2) = 0.332
Next, we can solve for cos(theta/2) by subtracting 1 from both sides:
-cos(theta/2) = 0.332 - 1
-cos(theta/2) = -0.668
To find theta/2, we can take the inverse cosine (arccos) of both sides:
theta/2 = arccos(-0.668)
Finally, we multiply theta/2 by 2 to obtain the value of theta:
theta = 2 * arccos(-0.668)
Using a calculator or mathematical software, you can find the numerical value of theta by substituting the equation into the calculator. The resulting value will be the angle theta in radians.