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ziro4ka [17]
3 years ago
7

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

Mathematics
2 answers:
ddd [48]3 years ago
7 0

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

vovangra [49]3 years ago
5 0

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}

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