Question

3 + 9Cost = 5 Sin^2 t решите пожалуйста уравнение!

Answer 1

5sin^2t - 9cost - 3 = 0
5*(1 - cos^2t) -  9cost - 3 = 0
-5cos^2t - 9cost + 2 = 0
5cos^2t  + 9cost - 2 = 0
D = 81 + 4*5*2 = 121
1)  cost = (-9 - 11)/10
cost = - 2 не удовлетворяет условию:  I cost I ≤ 1
2) cost = (-9 + 11)/10
cost = 1/5
t = (+ -)arccos(1/5) + 2πn, n∈Z
Ответ: t = (+ -)arccos(1/5) + 2πn, n∈Z