SOLUTION: Hi tutors, this is a extra points question for a quiz, but my professor never teaches us this kind of question. Find the exact general and particular solutions to the equation:

Algebra.Com
Question 1116853: Hi tutors, this is a extra points question for a quiz, but my professor never teaches us this kind of question.
Find the exact general and particular solutions to the equation:
10sin ( 3x+ pi/6 ) + 7sqrt(3) = 2sqrt(3)
1. What is the exact general solution?
2. What is the particular solutions in {0, 2pi }
can someone help me with this question ?
Found 2 solutions by Edwin McCravy, KMST:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


First subtract  from both sides:



Divide both sides by 10





The right side is negative.
The left side is a sine.
The sine is negative in QIII and QIV.
The 2 particular solutions in [0,2p) are,
from the unit circle 4p/3 and 5p/3. 

,   
,   
,   
,      
,       
                

The exact general solutions are found by adding 2p∙n
to the exact particular solutions in [0,2p),
where n is any integer positive, negative or 0.

So the general solutions are:

   

If you like you can do a little work on
those exact general solutions and get



Edwin
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
1. An exact general solution .
2. The particular solutions in
can found by using the formula above for
and for ,
and for , and
and for .

EXPLANATION AND GRAPHICAL REORESENTATION:
As Edwin showed you, simple algebra leads you to
.

What angles could measure ?

The angles and have
.
One whole counterclockwise turn is (radians),
.
Angles and measure less, and more than that,
or and respectively
A general formula for clockwise expression for the measure of or is
,
and a general formula for all angles co-terminal with those is
for any integer .
So, to find the exact general solution, with representing any integer





RANT:
In math, there is no such a thing as "this kind of question"
or "this kind of problem".
Unfortunately, too many math instructors and tutors
classify problems into hundreds or thousands of "kinds" or "types",
and then encourage students to memorize the classification,
and the corresponding problem-solving recipes.
That makes math into a no-reasoning memorization exercise similar to learning a foreign language.
Why?
Maybe because is easier than trying to persuade students that they only need to
1) understand a few simple concepts, and
2) apply those concepts and their own brains.
Maybe because they were taught math that same way,
and they do not know any better.
Or is it that they believe the students are incapable of reasoning?
RELATED QUESTIONS

Joe Tyson is the kicker for his college football team. Last season he kicked 38 times and (answered by josmiceli)
Stanbon, this isnt a math question but how do I become smart like you and the other... (answered by stanbon)
Hi, I'm trying to figure out how to set up this problem: Find the measure of an angle (answered by jim_thompson5910,Earlsdon)
Hello to all tutors, glad I found your site. I have checked approx 300 pages but... (answered by stanbon)
my math teacher gave us a question like this.....find out if the statement is... (answered by Alan3354,rfer)
This is my first time here not sure I picked the correct topic but here it is the... (answered by darq)
Could you help me with this question on my homework? My teacher gave us this problem but... (answered by lwsshak3)
Hi there! My name is Chelsea and I've never been very well at story problems. I can never (answered by richwmiller,solver91311)
A professor gives a 15 question MCQ quiz. For each question in the quiz, there are five... (answered by stanbon)