Question

2sin^2+3sinx=2 Pomogiteeeee pojaluista

Answer 1

заменить синХ на К. тогда выражение примет вид

2К²+3К-2=0   к= -3+-√(9+16)/4 ,  К1= -3-5/4=-2 , К2=-3+5/4 ,К2=1/2

первое решение не годится,синус меньше 1. а второе дает два ответа синус равне корню из 1/2  или √2/2  

Х1=п/4+2пм где м -любое целое число, или Х2=3п/4+2пм

Answer 2

I'm sorry, but the equation you provided is incomplete. Please double-check the equation and ensure that all terms and variables are included.

If you meant to write "2sin^2(x) + 3sin(x) = 2", then we can solve for x as follows:

Let's start by factoring the left-hand side of the equation:

2sin^2(x) + 3sin(x) - 2 = 0

(2sin(x) - 1)(sin(x) + 2) = 0

Now we can solve for sin(x) by setting each factor equal to zero:

2sin(x) - 1 = 0 or sin(x) + 2 = 0

Solving for sin(x) in the first equation:

2sin(x) - 1 = 0

2sin(x) = 1

sin(x) = 1/2

Taking the inverse sine of both sides, we get:

x = pi/6 + 2pin or x = 5pi/6 + 2pin where n is an integer.

Now solving for sin(x) in the second equation:

sin(x) + 2 = 0

sin(x) = -2

However, since the range of sine function is from -1 to 1, there are no real solutions to this equation.

Therefore, the solutions to the equation 2sin^2(x) + 3sin(x) = 2 are:

x = pi/6 + 2pin or x = 5pi/6 + 2pin where n is an integer.