SOLUTION: Hi, can I have help with this question: Solve cosx-3sinx=3. Do I need to work with general solutions? Can you help with explaining the process? Thank you

Algebra ->  Trigonometry-basics -> SOLUTION: Hi, can I have help with this question: Solve cosx-3sinx=3. Do I need to work with general solutions? Can you help with explaining the process? Thank you      Log On


   

Question 1203484: Hi, can I have help with this question:
Solve cosx-3sinx=3.
Do I need to work with general solutions? Can you help with explaining the process? Thank you
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

cos%5E%22%22%28x%29-3sin%5E%22%22%28x%29%22%22=%22%223

cos%5E%22%22%28x%29+%22%22=%22%22+3sin%5E%22%22%28x%29%2B3

cos%5E%22%22%28x%29+%22%22=%22%22+3%28sin%5E%22%22%28x%29%5E%22%22%2B1%29

Square both sides:

cos%5E2%28x%29%22%22=%22%229%28sin%5E2%28x%29%2B2sin%5E%22%22%28x%29%5E%22%22%2B1%29

1-sin%5E2%28x%29%22%22=%22%229sin%5E2%28x%29%2B18sin%5E%22%22%28x%29%2B9%29

0%22%22=%22%2210sin%5E2%28x%29%2B18sin%5E%22%22%28x%29%2B8

10sin%5E2%28x%29%2B18sin%5E%22%22%28x%29%2B8%22%22=%22%220

5sin%5E2%28x%29%2B9sin%5E%22%22%28x%29%2B4%22%22=%22%220

%28sin%5E%22%22%28x%29%5E%22%22%2B1%29%285sin%5E%22%22%28x%29%5E%22%22%2B4%29%22%22=%22%220



Were you asked to solve in degrees or radians?
Were you asked to find all solutions? Or just the smallest positive solutions?

Since we don't have answers to these questions, we can go no further.  So you
must finish.  Be sure to check for extraneous answers since we squared both
sides, which very often introduces extraneous answers we must discard. But this
is not necessarily the case.

Edwin