Question

Sin x = -0. 5√2 , 2cos2x-1=0

Answer 1

Ответ:

Sin x = 2cos,01

Объяснение:

Answer 2

To solve the equations sin(x) = -0.5√2 and 2cos(2x) - 1 = 0, you can follow these steps:

1. Solve for x in the first equation sin(x) = -0.5√2: Take the arcsin (inverse sine) of both sides: x = arcsin(-0.5√2)

2. Next, simplify the value of arcsin(-0.5√2): x ≈ -π/4 or x ≈ -3π/4

3. Now, you have two potential values for x, -π/4 and -3π/4. You'll need to check both values in the second equation to see which ones satisfy 2cos(2x) - 1 = 0:

   For x = -π/4: 2cos(2(-π/4)) - 1 = 2cos(-π/2) - 1 = 2(0) - 1 = -1 - 1 = -2

   For x = -3π/4: 2cos(2(-3π/4)) - 1 = 2cos(-3π/2) - 1 = 2(0) - 1 = -1 - 1 = -2

Both values of x, -π/4 and -3π/4, satisfy the equation 2cos(2x) - 1 = 0, and both result in -2. So, there are two solutions:

x = -π/4 and x = -3π/4.