Question

3sinx+4sin(pi/2+x)=0

Answer 1

3sinx+4cosx=0 |:cosx неравное 0
3tgx+4=0
tgx=-4/3
x=-arctg4/3+Пn, n∈Z

Answer 2

To solve the equation 3sinx + 4sin(π/2 + x) = 0, we can use the following trigonometric identities:

• sin(π/2 + x) = cos(x)
• sin(x) = cos(π/2 - x)

Substituting these identities into the equation, we get:

3sinx + 4cosx = 0

Dividing both sides by cosx (assuming cosx is not zero), we get:

3tanx + 4 = 0

Subtracting 4 from both sides, we get:

3tanx = -4

Taking the arctangent of both sides, we get:

x = atan(-4/3)

Using a calculator, we can evaluate atan(-4/3) to be approximately -0.93 radians or -53.13 degrees.

Therefore, the solution to the equation 3sinx + 4sin(π/2 + x) = 0 is x = -0.93 radians (or -53.13 degrees), assuming x is measured in radians.