Question

Solve 4 + 2 sinx= 14-8 sinx for 0° ≤ x ≤ 180

Answer 1

x= 90°.

Explanation:

1. Write the expression.

`4 + 2 sin(x)= 14-8 sin(x)`

2. Subtract "4" from both sides of the equation.

`-4+4 + 2 sin(x)= 14-8 sin(x)-4\\ \\2 sin(x)= 10-8 sin(x)`

3. Add "8sin(x)" to both sides of the equation.

`2 sin(x)+8 sin(x)= 10-8 sin(x)+8 sin(x)\\ \\10 sin(x)= 10`

4. Divide both sides by 10.

`(10 sin(x))/(10) = (10)/(10) \\ \\sin(x)=1`

5. Apply the arcsin of sin^-1 to both sides of the equation.

`arcsin(sin(x))=arcsin(1)\\ \\x=90`

6. Conclude.

x= 90°.