Final answer:
To solve the inequality cos^2(x) - (3/4) < 0.05, we can start by factoring out the common factor of cos^2(x) - (3/4) to get (cos(x) - 1/2)(cos(x) + 3/2) < 0.05. The solution is δ > cos^(-1)(1/2) + 6.
Step-by-step explanation:
To solve the inequality cos^2(x) - (3/4) < 0.05, we can start by factoring out the common factor of cos^2(x) - (3/4) to get (cos(x) - 1/2)(cos(x) + 3/2) < 0.05. Now, we have to consider two cases:
Case 1: cos(x) - 1/2 < 0 and cos(x) + 3/2 > 0
Solve the first inequality by adding 1/2 to both sides: cos(x) < 1/2. The solution to this inequality is cos^(-1)(1/2) + 6. Therefore, δ > cos^(-1)(1/2) + 6.
Case 2: cos(x) - 1/2 > 0 and cos(x) + 3/2 < 0
Solve the second inequality by subtracting 3/2 from both sides: cos(x) < -3/2. However, there are no solutions to this inequality because the cosine function's range is between -1 and 1. Therefore, we only need to consider Case 1.