Show your steps. Solve the equation in the interval from 0 to 2π. Round to the nearest hundredth. 7cos(2t) = 3

Answer 1

To solve for t in the interval from 0 to 2π we can use inverse cosine (cos⁻¹) and the following steps:
1. Divide both sides by 7: cos(2t) = 3/7
2. Take the inverse cosine of both sides: cos⁻¹(cos(2t)) = cos⁻¹(3/7)
3. Simplify: 2t = ±0.9344 + 2πn or 2t = ±2.207 + 2πn, where n is an integer
4. Solve for t: t = 0.4672 + πn or t = 1.1035 + πn, where n is an integer

Therefore, the solutions in the interval from 0 to 2π are:
t ≈ 0.47, 1.10, 2.68, 3.31, 4.89, and 5.53.