Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separat?
10 sin2(x) = 5
and
4 cos(x) + 2 sin(2x) = 0
Please help me with these two problems. Thank you!
Update:Thank you! The second question was right, but the first question involving 10 sin2(x) = 5, seems to be coming up incorrect on my web assignment.
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TOO MANY PARENTHESES!!
sin 2x = 1/2
2x = π/6, 5π/6, 13π/6, 17π/6
x = π/12, 5π/12, 13π/12, 17π/6
4 cos x + 2 sin 2x = 0
4 cos x + 2 (2 sin x cos x) = 0
4 cos x + 4 sin x cos x = 0
4 cos x (1 + sin x) = 0
4 cos x = 0 or 1 + sin x = 0
cos x = 0.........sin x = -1
x = π/2 or 3π/2.......x = 3π/2
x = π/2, 3π/2
first equation (sin x)^2 = a million- (cos x)^2 so it is going to become 2 - 2 (cos x)^2 - cos x - a million = 0 or 2 (cos x)^2 + cos x - a million = 0 or (2 cos x + a million) (cos x - a million) = 0 from which you get cos x = - a million/2 or cos x = a million from the 1st, you get x = pi*2/3 or pi*5/3, from the 2d, x = 0 or 2pi further you could resolve the 2d as (cosx - 9) (cosx +a million) = 0 it has in basic terms one element cos x + a million = 0 so x = pi