Question

4sin^2 x+11sin x+7=oпомогите пожалуйста

Answer 1

Sinx=t

4t+11t+7=0

D=121-4*7*4=9=3²
t1=-11+3/8=-1
t2=-11-3/8=-14/8 Не имеет значения 

sinx=-1
х = 3п/2 + 2пк

Answer 2

Solving the Equation 4sin^2(x) + 11sin(x) + 7 = 0

To solve the equation 4sin^2(x) + 11sin(x) + 7 = 0, we can use the quadratic formula or factorization. Let's use the quadratic formula to find the solutions for the given equation.

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 4, b = 11, and c = 7. Substituting these values into the quadratic formula, we get:

x = (-11 ± √(11^2 - 4*4*7)) / (2*4)

Calculating the discriminant (b^2 - 4ac):

Discriminant = 11^2 - 4*4*7 = 121 - 112 = 9

Now, substituting the discriminant into the quadratic formula:

x = (-11 ± √9) / 8

So, the solutions for the given equation are:

x = (-11 + 3) / 8 = -8 / 8 = -1

x = (-11 - 3) / 8 = -14 / 8 = -1.75

Therefore, the solutions for the equation 4sin^2(x) + 11sin(x) + 7 = 0 are x = -1 and x = -1.75.