# Thread: Moving onto trigo equations :(

1. ## Moving onto trigo equations :(

equation of a line is $\displaystyle y = 3sin2x + 2cos^2x$ 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!

2. Originally Posted by Punch
equation of a line is $\displaystyle y = 3sin2x + 2cos^2x$ 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!
$\displaystyle 0 \le x < 360$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$\displaystyle \tan{x} = 3$

$\displaystyle x = \arctan(3)$

$\displaystyle x = \arctan(3) + 180$