Question

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

Answer 1

Answer:

x= 90°.

Step-by-step 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.

$\frac{10 sin(x)}{10} = \frac{10}{10} \\ \\sin(x)=1$

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

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

6. Conclude.

x= 90°.