SOLUTION: Determine how many solutions there are for the equation: 2sin x + 3cos x= 2

Algebra ->  Trigonometry-basics -> SOLUTION: Determine how many solutions there are for the equation: 2sin x + 3cos x= 2       Log On


   

Question 1083018: Determine how many solutions there are for the equation:
2sin x + 3cos x= 2
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
There are infinitely many solutions.  I will assume that
you were asking how many solutions there are in the interval
matrix%281%2C5%2C%22%5B%22%2C0%2C%22%2C%22%2C2pi%2C%22%29%22%29


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

2sin%5E%22%22%28x%29+%2B+3sqrt%281-sin%5E2%28x%29%29=2

3sqrt%281-sin%5E2%28x%29%29=+2-2sin%5E%22%22%28x%29

9%281-sin%5E2%28x%29%29=4-8sin%5E%22%22%28x%29%2B4sin%5E2%28x%29

9-9sin%5E2%28x%29=4-8sin%5E%22%22%28x%29%2B4sin%5E2%28x%29

-13sin%5E2%28x%29%2B8sin%5E%22%22%28x%29%2B5=0

13sin%5E2%28x%29-8sin%5E%22%22%28x%29-5=0






There are 2 solutions in the interval matrix%281%2C5%2C%22%5B%22%2C0%2C%22%2C%22%2C2pi%2C%22%29%22%29
for the one crossed out is extraneous and doesn't check.
The other two do.

Edwin