show all solutions on the given interval [0, 2pi)
C ceason2011 New member Joined Apr 22, 2011 Messages 1 Apr 22, 2011 #1 show all solutions on the given interval [0, 2pi)
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Apr 22, 2011 #2 Write the equation in terms of sin or cos alone. Then, solve for x. i.e. in terms of sin alone: \(\displaystyle 3(1-sin^{2}(x))-sin^{2}(x)=0\) Now, continue?. It would appear there are 4 solutions in the given interval. Graphing helps. Remember, the period of sin or cos.
Write the equation in terms of sin or cos alone. Then, solve for x. i.e. in terms of sin alone: \(\displaystyle 3(1-sin^{2}(x))-sin^{2}(x)=0\) Now, continue?. It would appear there are 4 solutions in the given interval. Graphing helps. Remember, the period of sin or cos.
D Deleted member 4993 Guest Apr 22, 2011 #3 ceason2011 said: show all solutions on the given interval [0, 2pi) Click to expand... or you could continue from \(\displaystyle 3cos^2(x) \ - \ [1 \ - \ cos^2(x)] \ = \ 0\)
ceason2011 said: show all solutions on the given interval [0, 2pi) Click to expand... or you could continue from \(\displaystyle 3cos^2(x) \ - \ [1 \ - \ cos^2(x)] \ = \ 0\)
