- #1
agentc0re
- 2
- 0
Homework Statement
sin(2x)-cos(2x)=sqrt(2)sin(2x+Api), then the number 0 < A = ____ < 2
Homework Equations
http://bit.ly/9njiUW <-- trig reference sheet with formulas and identites
The Attempt at a Solution
So I start with the left side of the equation and attempt to make it look like the right in order to figure out what A is. Using some identities i started out:
2sin(x)cos(x) - cos^2(x) + sin^2(x)
2sin(x)cos(x) - ( 1 - sin^2(x) ) + sin^2(x)
2sin(x)cos(x) - 1 + sin^2(x) +sin^2(x)
2sin(x)cos(x) - 1 + 2sin^2(x)
2( 1/2[ sin(x + x) + sin(x - x) ] ) - 1 + 2sin^2(x)
sin(x + x) + sin(x - x) - 1 + 2sin^2(x)
sin(2x) + sin(0) - 1 + 2sin^2(x)
sin(2x) + 0 - 1 + 2sin^2(x)
sin(2x) -1 + 2sin^2(x)
Then I realized I made a big loop with the "sin(2x)" part and am not sure how to go from there.