solve the equation in the interval from 0 to 2π, 4cos(t)=3

Answer 1

To solve the equation 4cos(t) = 3 in the interval from 0 to 2π, we need to isolate the variable t.

First, divide both sides by 4:
cos(t) = 3/4

Now, we need to find the angles where the cosine function equals 3/4. In the interval from 0 to 2π, the cosine function is positive in the first and fourth quadrants.

To find the angles where cos(t) = 3/4 in the first quadrant, we can use the inverse cosine function:
t = cos^(-1)(3/4)
t ≈ 0.7227 radians

To find the angle in the fourth quadrant, we need to borrow the angle from the first quadrant:
t = 2π - 0.7227
t ≈ 5.5608 radians

Therefore, the solutions in the interval from 0 to 2π are approximately 0.7227 radians and 5.5608 radians.