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Kamikadze1997
@Kamikadze1997
August 2022
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Sin(5x+pi/6) = 1/2
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dnepr1
Verified answer
Общий вид решения уравнения
sin x
= a,
где |
a
| ≤ 1, определяется формулой:
x = (- 1)^k
· arcsin(a) +
πk,
k ∈ Z (целые числа
).
Sin(5x+pi/6) = 1/2
5x+pi/6 = Arc sin(1/2) = (π/6)+2πk
5x = -(π/6)+(π/6)+2πk = 2πk.
х₁ = (2/5)πk.
5x+pi/6 = Arc sin(1/2) = (5π/6)+2πk
5x = -(π/6)+(5π/6)+2πk =(2π/3)+ 2πk.
х₂ = (2π/15)+2πk/5
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Answers & Comments
Verified answer
Общий вид решения уравнения sin x = a, где | a | ≤ 1, определяется формулой:x = (- 1)^k · arcsin(a) + πk, k ∈ Z (целые числа).Sin(5x+pi/6) = 1/2
5x+pi/6 = Arc sin(1/2) = (π/6)+2πk
5x = -(π/6)+(π/6)+2πk = 2πk.
х₁ = (2/5)πk.
5x+pi/6 = Arc sin(1/2) = (5π/6)+2πk
5x = -(π/6)+(5π/6)+2πk =(2π/3)+ 2πk.
х₂ = (2π/15)+2πk/5