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double angle identity help!?
solve for θ, [0,2pi]
2cos2θ +1=0?show work please
3 Answers
- ted sLv 712 months agoFavorite Answer
OR you remember that cos 2Θ = 2 cos² Θ - 1 to lead to cos² Θ = 1/4 ===> cos Θ = ± 1 / 2 ===> Θ = π / 3 , 2π/3 , 4π / 3 , 5π / 3
- 12 months ago
cos2θ = -1/2
Where is cosθ = -1/2?
120 degrees and 240 degrees or...
2pi/3 and 4pi/3
Divide by 2 to account for the difference between cos(2θ) and cos(θ)
You get 60 degrees and 120 degrees or...
pi/3 and 2pi/3
We know that the k value of cos(2θ) is 2, so the period is P = 2pi / k = 2pi / 2 = pi
Add pi = 3pi/3 to each solution, and be mindful of the interval [0,2pi]
Answers:
pi/3
4pi/3
2pi/3
5pi/3
