Find all real numbers on the interval [0,2pi) that satisfies the equation: sin2xcosx-cos2xsinx= - 1/2
help me out with this please if you can (:
2007-03-12 09:10:13 · 3 answers · asked by MeganElizabeth 5 in Science & Mathematics ➔ Engineering
Do your own homework!
2007-03-12 09:18:03 · answer #1 · answered by Anonymous · 1⤊ 1⤋
I used Microsoft Excel to plot the terms on the left hand side. The plot looks very similar to a sine wave of amplitude +/-1 and period of 2pi.
The curve crosses -0.5 at approximately 3.6 and 5.7
Narrowing down the search, I came up with 3.66519 and 5.75959
This is a "graphical" solution not a numeric solution. Your teacher might not like it.
.
2007-03-12 12:11:51 · answer #2 · answered by tlbs101 7 · 0⤊ 0⤋
Begin with the identity: sin(a + b) = sin(a)cos(b) + sin(b)cos(a)
In your expression, a = 2x and b = -x so:
sin(2x)cos(x) - cos(2x)sin(x) = sin(2x - x) = sin(x)
Of course, sin(x) = -1/2 at 7/6 pi and 11/6 pi
2007-03-12 12:41:01 · answer #3 · answered by Pretzels 5 · 0⤊ 0⤋