Question

Find the zeros of the function in the interval (-2π, 2π) of -5sin(2x).

a) x = -π/2, x = π/2
b) x = -π, x = π
c) x = -3π/2, x = 3π/2
d) x = -2π, x = 2π

Answer 1

The zeros of the function -5sin(2x) in the interval (-2π, 2π) are the values for which the sine function is zero, that is, at x = -π, 0, and π. Among the options provided, option (b) which includes x = -π and x = π is correct.

Step-by-step explanation:

To find the zeros of the function -5sin(2x) in the interval (-2π, 2π), we look for the values of x for which sin(2x) = 0. Since we know that the sine function oscillates between +1 and -1 and is zero at multiples of π, we have sin(2x) = 0 when 2x is a multiple of π, or 2x = nπ where n is an integer.

Dividing both sides by 2, we get x = n(π/2). To find the zeros within our specified interval, we consider the multiples n that fall within the range of -2π to 2π when multiplied by π/2.

The relevant multiples are -4, -2, 0, 2, and 4. Therefore, the zeros of the function are at x = -2π, -π, 0, π, and 2π. Hence, the correct zeros within the given interval are: x = -π, 0, and π. However, among the multiple choice options provided, x = 0 is not listed, so we can only choose between the given options. Option (b) x = -π, x = π is the correct answer as it includes the zeros within the provided options that fall in the interval (-2π, 2π).