Question

Solve the trigonometric equation for all values 0 ≤ x < 6 for cos(π/3 * x) - 1 = 0. What are the solutions?

a) x = 0, x = 3
b) x = 1, x = 2
c) x = 1, x = 5
d) x = 2, x = 4

Answer 1

The values that satisfy the trigonometric equation cos(π/3 * x) - 1 = 0 within the specified domain are x = 0 and x = 2.

Step-by-step explanation:

To solve the trigonometric equation cos(π/3 * x) - 1 = 0, we need to find the values of x for which the cosine function equals 1. Remember that the cosine of 0 is 1, thus we can determine that the argument of the cosine function π/3 * x must equal 0 or a multiple of 2π within the given domain of 0 ≤ x < 6 because the cosine function is periodic with a period of 2π. Setting the argument of the cosine to 0 and 2π, we get:

x = 0 (since π/3 * 0 = 0)
x = 2 (since π/3 * 2 = 2π/3)

Checking for multiples of 2π up to the domain specified:

• π/3 * 6 = 2π (exceeds x < 6)

Thus, the values in the specified domain that satisfy the equation are x = 0 and x = 2. The correct choice would be x = 2 (as x = 6 is not within the specified domain), making the other given options incorrect.