Solve for x?
1 and 5 are both difference of two squares...
5) (2sinx)^2=1
sinx= +- sqrt(1/2)
x = +- 30 deg
others are quadratics, factor. On 4 dont forget the sollution sinx=0
1. 4 sin^2x – 1 = 0
2. 2 sin^2x + sin x = 1
3. 2 sin^2x + 7 sin x = 4
4. cos x sin x + sin x = 0
5. 2 sin^2x - 1 = 0
2 answers
I'll pick another, how about #3 ?
2 sin^2x + 7 sin x = 4
2 sin^2x + 7 sin x - 4 = 0
You should recognize this as a quadratic this factors like bob suggested,
e.g.
2y^2 + 7y - 4 = 0 , in your case y = sinx
(2y - 1)(y + 4) = 0
y = 1/2 or y = -4
then (2sinx - 1)(sinx + 4) = 0
sinx = 1/2 or sinx = -4, but you know sinx has to always fall between -1 and +1
sinx = 1/2
by the CAST rule, x must be in either quadrant I or II
x = 30° OR x = 180-30 or 150°
2 sin^2x + 7 sin x = 4
2 sin^2x + 7 sin x - 4 = 0
You should recognize this as a quadratic this factors like bob suggested,
e.g.
2y^2 + 7y - 4 = 0 , in your case y = sinx
(2y - 1)(y + 4) = 0
y = 1/2 or y = -4
then (2sinx - 1)(sinx + 4) = 0
sinx = 1/2 or sinx = -4, but you know sinx has to always fall between -1 and +1
sinx = 1/2
by the CAST rule, x must be in either quadrant I or II
x = 30° OR x = 180-30 or 150°