SOLUTION: Solve for the GENERAL solution : 3= 2sin (3(x+ (pi/3)) +4

Question 1173665: Solve for the GENERAL solution : 3= 2sin (3(x+ (pi/3)) +4
Found 2 solutions by jsmallt9, ikleyn:
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
1) To find a general solution, first use algebra to transform the equation into the form:
trigfunction(something) = number

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

Subtracting 4 from each side we get:
-1 = 2sin (3(x+ (pi/3))

Dividing both sides by 2 we get:
-1/2 = sin (3(x+ (pi/3))
which is the desired form.

2) Next, we need to find expressions for angles whose sin's are -1/2. Since sin(pi/6) = 1/2 the reference angle is pi/6. And since sin is negative in the 3rd and 4th quadrants, we are looking for angles in those quadrants with a reference of pi/6.

In the third quadrant our expression would be:
pi + pi/6 + 2pi*n
which simplifies to:
7pi/6 + 2pi*n

In the fourth quadrant our expression would be:
2pi - pi/6 + 2pi*n
which simplifies to:
11pi/6 + 2pi*n

NOTE: The 2pi*n is a way for us to include all the coterminal angles (which would also all have sin values of -1/2. The "n" can be replace by any integer. Each different integer results in another angle whose sin is -1/2.

3) Write equations to set the trig function's argument to the expressions from step 2:

3(x+ (pi/3)) = 7pi/6 + 2pi*n
which simplifies to
3x + pi = 7pi/6 + 2pi*n

3(x+ (pi/3)) = 11pi/6 + 2pi*n
which simplifies to
3x + pi = 11pi/6 + 2pi*n

4) Solve these equations for x.
Subtracting pi from each side of both equations:
3x = pi/6 + 2pi*n
3x = 5pi/6 + 2pi*n

Multiplying each side by 1/3 (or dividing both sides by 3) we get:
x = pi/18 + (2/3)pi*n
x = 5pi/18 + (2/3)pi*n

These last equations are the "general solution".
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

The equation in the post is

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

This equation is written INCORRECTLY.

It has three opening parentheses and only two closing parentheses.

THEREFORE, my advise to a person who created this post is to fix this FATAL ERROR, then re-post to the forum.

If you re-post, then PLEASE do not post it to me personally.

Re-post to the forum, as you post it regularly.

I insistently recommend you to re-post, because the solution which you got from another tutor,
is INCOMPLETE and therefore INCORRECT.

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