What are the angles for 2cos2x=-1?
回答 (3)
2016-11-10 9:38 pm
✔ 最佳答案
cos 2x = - 1/22x = 120⁰ , 240⁰ , 480⁰ . 600⁰
x = 60⁰ , 120⁰ , 240⁰ , 300⁰
2016-11-10 9:36 pm
2cos(2x) = -1
∴ cos(2x) = -1/2
given cos(θ) = x then θ = 2πn ± cos⁻¹(x), where n∈ℤ [note n∈ℤ means n is a member of the set of integers]
∴ 2x = 2πn ± cos⁻¹(-1/2), where n∈ℤ
∴ 2x = 2πn ± 2π/3, where n∈ℤ
∴ x = πn ± π/3, where n∈ℤ
over the interval of 0 ≤ x < 2π
∴ x = π/3, 2π/3, 4π/3 and 5π/3
∴ cos(2x) = -1/2
given cos(θ) = x then θ = 2πn ± cos⁻¹(x), where n∈ℤ [note n∈ℤ means n is a member of the set of integers]
∴ 2x = 2πn ± cos⁻¹(-1/2), where n∈ℤ
∴ 2x = 2πn ± 2π/3, where n∈ℤ
∴ x = πn ± π/3, where n∈ℤ
over the interval of 0 ≤ x < 2π
∴ x = π/3, 2π/3, 4π/3 and 5π/3
2016-11-10 10:06 pm
2cos2x = -1
x = -1/(2cos2)
I suspect you really meant 2cos(2x) or 2cos^2x but which?
x = -1/(2cos2)
I suspect you really meant 2cos(2x) or 2cos^2x but which?
收錄日期: 2021-04-22 00:01:19
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