Question

Find all solutions of the equation in the interval [0, 2 pi) 2 cos0-1=0

Answer 1

Answer:

θ = π/3, 5π/3

Step-by-step explanation:

2 cos θ - 1 = 0

2 cos θ = 1

cos θ = 1/2

θ = π/3, 5π/3

Answer 2

ANSWER

EXPLANATION

The given trigonometric equation is:

$2 \cos( \theta) - 1 = 0$

$\implies \: 2 \cos( \theta) = 1$

$\implies \: \cos( \theta) = \frac{1}{2}$

The cosine ratio is positive in the first and fourth quadrants.

In the first quadrant,

$\theta = \cos ^{ - 1} ( \frac{1}{2})$

$\theta = \frac{\pi}{3}$

In the fourth quadrant,

$\theta =2 \pi - \cos ^{ - 1} ( \frac{1}{2})$

$\theta =2 \pi - \frac{\pi}{3}$

$\theta = \frac{5\pi}{3}$

Therefore on the interval, [0,2π] the solution to the given trigonometric equation is:

$\theta = \frac{\pi}{3} \: and \: \frac{5\pi}{3}$