Math  /  Trigonometry

QuestionSolve the equation. Give all solution in 0θ<2π0 \leq \theta<2 \pi 2cos(θ)=12 \cos (\theta)=1
Select all that apply 0 π2\frac{\pi}{2} π\pi 3π2\frac{3 \pi}{2} π6-\frac{\pi}{6} π6\frac{\pi}{6} 2π3\frac{2 \pi}{3} 7π6\frac{7 \pi}{6} 5π3\frac{5 \pi}{3} π4-\frac{\pi}{4} π4\frac{\pi}{4} 3π4\frac{3 \pi}{4} 5π4\frac{5 \pi}{4} 7π4\frac{7 \pi}{4} π3-\frac{\pi}{3} π3\frac{\pi}{3} 5π6\frac{5 \pi}{6} 4π3\frac{4 \pi}{3} 11π6\frac{11 \pi}{6} π2-\frac{\pi}{2}

Studdy Solution
Verify that these solutions are within the interval 0θ<2π 0 \leq \theta < 2\pi .
- π3\frac{\pi}{3} is within the interval 0θ<2π 0 \leq \theta < 2\pi . - 5π3\frac{5\pi}{3} is also within the interval 0θ<2π 0 \leq \theta < 2\pi .
The solutions to the equation 2cos(θ)=1 2 \cos(\theta) = 1 in the interval 0θ<2π 0 \leq \theta < 2\pi are:
π3,5π3 \boxed{\frac{\pi}{3}, \frac{5\pi}{3}}

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