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

User Praveen
by
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1 Answer

14 votes
14 votes

Answer:

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°.

User Triveni Badgujar
by
3.3k points