Question

Sin x/2•cos x/2=1/4. Pliz

Answer 1

Ответ:

sinx/2•cosx/2=1/4

sinx/2=1/4

4sinx=2

sinx=1/2

Answer 2

To solve the equation sin(x/2) * cos(x/2) = 1/4, we can use the double-angle identity for sine:

sin(2θ) = 2sin(θ)cos(θ)

Let's apply this identity to the given equation:

sin(x/2) * cos(x/2) = 1/4

Using the double-angle identity, we can rewrite sin(x/2) * cos(x/2) as sin((x/2) * 2):

2 * sin(x/2) * cos(x/2) = 1/4

sin(x) = 1/4

Now, we have sin(x) = 1/4. To find the values of x that satisfy this equation, we can take the inverse sine (also known as arcsin) of both sides:

x = arcsin(1/4)

Using a calculator, we can find the approximate value of arcsin(1/4):

x ≈ 14.4775 degrees + 360n or x ≈ 165.5225 degrees + 360n

Here, n is an integer that represents the full set of solutions. The "+ 360n" allows us to account for the periodic nature of the trigonometric functions, as sin(x) repeats itself every 360 degrees.

Therefore, the solutions for x are approximately:

x ≈ 14.4775 degrees, 165.5225 degrees, 374.4775 degrees, 515.5225 degrees, and so on.

Please note that these values are approximate, and there are infinitely many solutions due to the periodicity of the sine function.