Find all values of x in the interval [0, 2π]

Question

hat satisfy the equation. 10 cos(x) − 5 = 0?

Answer 1

The trigonometric equation 10 cos(x) - 5 = 0

10 cos(x) = 5

cos (x) = 5/10

cos (x) = 1/2

cos (x) = cos (π/3)

Principal value is x = π/3

The genaral solution of cos(θ) = cos(α) is θ = 2nπ ± α, where n is an integer.

x = 2nπ ± (π/3)

If n = 0, x = 2(0)π + (π/3) and x = 2(0)π - (π/3) = π/3 and - π/3.

If n = 1, x = 2(1)π + (π/3) and x = 2(1)π - (π/3) = 2π + π/3 and 2π - π/3 = 7π/3 and 5π/3.

Therefore, the solutions of the given equation are x = π/3, x = 5π/3 and x = 7π/3 in the interval [0, 2π].