Answer:
the solution to the trigonometric inequality cos(0.65x) > 0.44 over the interval 0 ≤ x < 4.834.
Explanation:
The given inequality is:
cos(0.65x) > 0.44
To solve this inequality, we need to isolate the variable x.
First, let's take the inverse cosine (arccos) of both sides to remove the cosine function:
arccos(cos(0.65x)) > arccos(0.44)
Since the range of the inverse cosine function is limited to [0, π], we can rewrite the inequality as:
0 ≤ 0.65x < π
Now, let's solve for x by dividing each part of the inequality by 0.65:
0/0.65 ≤ x < π/0.65
Simplifying, we have:
0 ≤ x < π/0.65
Now, let's calculate the approximate value of π/0.65 to determine the interval for x:
π/0.65 ≈ 4.834
i hope i helped!