2 Answers

Leninhasda · Answer 1 · 2019-07-04T12:11:24+0000

Let's solve the sine equation.

1. Express sine function in the left side of equation:

$2\sin (4x)+6=5,\\ 2\sin (4x)=5-6,\\ 2\sin (4x)=-1,\\ \\ \sin (4x)=-(1)/(2)$ .

2. Use the genereal solution to get the solution of your equation:

$4x=(-1)^n\arcsin \left(-(1)/(2)\right) +2\pi n$ , where
$n\in Z$ .

3. Find
$\arcsin \left(-(1)/(2)\right)$ :

$\arcsin \left(-(1)/(2)\right)=-(\pi)/(3)$ .

4. Substitute part 3 into part 2 and express x:

$4x=(-1)^n \left(-(\pi)/(3)\right) +2\pi n$ , where
$n\in Z,$

$x=(-1)^(n+1)\cdot (\pi)/(12)+(\pi n)/(2)$ , where
$n\in Z$ .

5. Solutions of your equation are:

$x=(-1)^(n+1)\cdot (\pi)/(12)+(\pi n)/(2)$ , where
$n\in Z$ .

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