There lived an astronomer who was very much involved in his observations.
He often used to look up at the sky at night and start observing the stars.
Once, as he walked looking up at the stars, his leg slipped and he fell into a ditch. He started shouting.
A passer-by, who heard his shouts, helped him out of the ditch and asked, "How did you fall into this ditch?" The astronomer replied, “I was so engrossed in my observations that I did not notice the ditch".
The passer-by asked, "How do you expect to discover things when you fail to take note of things under your nose?" The astronomer walked away with a sad face.
Cos 2x можно выразить только через косинус, или только через синус, или через обе функции. cos 2x = 2cos^2 x - 1 = 1 - 2sin^2 x = cos^2 x - sin^2 x Нас интересует - через синус. 3 - 6sin^2 x - 5sin x + 1 = 0 Умножаем все на -1 6sin^2 x + 5sin x - 4 = 0 Квадратное уравнение относительно синуса D = 5^2 - 4*6(-4) = 25 + 96 = 121 = 11^2 sin x = (-5 - 11)/12 = -16/12 < -1 - не подходит sin x = (-5 + 11)/12 = 6/12 = 1/2 x = pi/6 + 2pi*k x = 5pi/6 + 2pi*k
There lived an astronomer who was very much involved in his observations.
He often used to look up at the sky at night and start observing the stars.
Once, as he walked looking up at the stars, his leg slipped and he fell into a ditch. He started shouting.
A passer-by, who heard his shouts, helped him out of the ditch and asked, "How did you fall into this ditch?" The astronomer replied, “I was so engrossed in my observations that I did not notice the ditch".
The passer-by asked, "How do you expect to discover things when you fail to take note of things under your nose?" The astronomer walked away with a sad face.
Пошаговое объяснение:
думаю правильно
cos 2x = 2cos^2 x - 1 = 1 - 2sin^2 x = cos^2 x - sin^2 x
Нас интересует - через синус.
3 - 6sin^2 x - 5sin x + 1 = 0
Умножаем все на -1
6sin^2 x + 5sin x - 4 = 0
Квадратное уравнение относительно синуса
D = 5^2 - 4*6(-4) = 25 + 96 = 121 = 11^2
sin x = (-5 - 11)/12 = -16/12 < -1 - не подходит
sin x = (-5 + 11)/12 = 6/12 = 1/2
x = pi/6 + 2pi*k
x = 5pi/6 + 2pi*k
Отрезку [Pi; 5pi/2] принадлежит корень:
x1 = pi/6 + 2pi = 13pi/6