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

Answer 1

We can start by isolating cos(2t) by dividing both sides by 7:

cos(2t) = 3/7

Next, we can use the inverse cosine function to solve for 2t:

2t = ±cos⁻¹(3/7)

Using a calculator, we find that cos⁻¹(3/7) is approximately 1.0201 radians. So:

2t = ±1.0201 + 2πn or 2t = ±(2π - 1.0201) + 2πn

where n is an integer. We can simplify this to:

t = ±0.5101 + πn or t = ±2.1200 + πn

Rounding to the nearest hundredth and plugging in n=0, 1, and 2, we get the following solutions in the interval from 0 to 2π:

t ≈ 0.51, 3.63 or t ≈ 2.12, 5.24

Therefore, the solutions to the equation 7cos(2t) = 3 in the interval from 0 to 2π are approximately 0.51, 2.12, 3.63, and 5.24.