# Moving onto trigo equations :(

• Dec 27th 2009, 04:36 AM
Punch
Moving onto trigo equations :(
equation of a line is $y = 3sin2x + 2cos^2x$ where 0 < X < 360

Calculate value for which the curve

a) meets the x-axis b) meets the line y = 2

I know that I have to simplify the equation and sub in y=0 and y=2, however I can't solve the equation.. thanks in advance!
• Dec 27th 2009, 05:30 AM
skeeter
Quote:

Originally Posted by Punch
equation of a line is $y = 3sin2x + 2cos^2x$ where 0 < X < 360

Calculate value for which the curve

a) meets the x-axis b) meets the line y = 2

I know that I have to simplify the equation and sub in y=0 and y=2, however I can't solve the equation.. thanks in advance!

$0 \le x < 360$

$3\sin(2x) + 2\cos^2{x} = 0$

$3(2\sin{x}\cos{x}) + 2\cos^2{x} = 0$

$2\cos{x}(3\sin{x} + cos{x}) = 0$

$\cos{x} = 0$ ... $x = 90$ , $x = 270$

$3\sin{x} = -\cos{x}
$

$\tan{x} = -\frac{1}{3}$

$x = \arctan\left(-\frac{1}{3}\right) + 180$

$x = \arctan\left(-\frac{1}{3}\right) + 360$

$3\sin(2x) + 2\cos^2{x} = 2$

$3(2\sin{x}\cos{x}) = 2 - 2\cos^2{x}$

$6\sin{x}\cos{x} = 2(1 - \cos^2{x})$

$6\sin{x}\cos{x} = 2\sin^2{x}$

$3\sin{x}\cos{x} - \sin^2{x} = 0$

$\sin{x}(3\cos{x} - \sin{x}) = 0$

$\sin{x} = 0$ ... $x = 0$ , $x = 180$

$3\cos{x} = \sin{x}$

$\tan{x} = 3$

$x = \arctan(3)$

$x = \arctan(3) + 180$