Hello! I can help you with this math problem.
To solve the equation j(x) = 0 for values of x in the interval [0, 2], we need to find the x-values where cos(x) = 0 in the given interval. The cosine function equals 0 at specific points. In the interval [0, 2], the cosine function equals 0 at x = π/2 and x = 3π/2. So, the solution to j(x) = 0 in the interval [0, 2] is x = π/2 and x = 3π/2.
Now, let's solve the equation k(x) for values of x in the domain of k. The function k(x) = sin(2x) involves the sine function with an argument of 2x. The sine function equals 0 at specific points. To find the values of x where sin(2x) = 0, we need to determine where the sine function with argument 2x equals 0. The sine function equals 0 when the argument is a multiple of π. Therefore, sin(2x) = 0 when 2x = nπ, where n is an integer.
Solving for x, we get x = nπ/2 for n being an integer. This means that for any integer value of n, sin(2x) will be equal to 0 at x = nπ/2.
I hope this explanation helps you understand how to solve these equations. If you have any more questions or need further clarification, feel free to ask!
