Matematické Fórum

Vubec nevim

Cus,
v pondeli pisu test na goniometricke rovnice a nerovnice. Budou to priklady z ucebnice - 30 cviceni. Vubec nevim jak to pocitat. Zkusim sem dat ty posledni priklady z kazdeho cviceni. I kdyz nevim jestli bude nekdo chtit pocitat 30 prikladu :-(.
$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=sin(4x-\frac{\prod}{3})%3D\sqrt{2}$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=tg^2%20x%2B3cotg^2x-4%3D0$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=(tgx%2Bcotbx)^2-(tgx-cotgx)^2%20%3D4%0A$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=3tg^4%203x%2B1%3D4tg^23x%20%0A$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=\sqrt{2}cosx-cotgx-\sqrt{2}sinx%2B1%3D0$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=4cosx%3D3sinx$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=7sin^2x%2B10cos^2%20x-11sinxcosx%3D5$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=2sin^2%20x%2Bsin^2%202x%3D2$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=sin^6%20x%2Bcos^6x%3D\frac{1}{4}%20sin^2%202x$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=sin^6%20x-cos^6x%3D%20cos%202x$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=1-cos2x%3Dsin2xsinx$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=\frac{1}{cos^22x%20}-2tg2x%3D0$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=cos4x-3cos2x-sin2x%3D0$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=tg3x-2sin6x%3D0$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=\sqrt{3}sin\frac{x}{4}-sin\frac{x}{2}%3D0$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=cos3x-sin3x%3Dcos2x-sin2x$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=sin(x%2B\frac{\prod}{4})cos(x%2B\frac{\prod}{4})%3D\frac{1}{4}%0A$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=4sinx%2B2cosx%3D\sqrt{2}%0A$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=tg(\frac{\prod}{2}%2Bx)-cotg^2x%3D\frac{cos2x-1}{sin^2x%20}%0A$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=sin(2x%2By)%3D\frac{1}{2}\sqrt{3}%0A$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=0%20\le%20cosx%3C\frac{1}{2}%0A$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=cos%20\frac{x}{2}%0A%20%3E0$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=tgx\ge%20cotgx$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=cos2x%2Bsinx%3C%20%201$

$http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=sin^2x%2B2sinxcosx%2Bcos^2%20x%3E\frac{1}{2}$

Diky za kazdej priklad :-)

gadgetka · 06. 06. 2009 18:09

7. příklad
návod:
$7\sin^2 x+10\cos^2 x-11\sin x\cos x=5\nl7\sin^2 x+10\cos^2 x-11\sin x\cos x=5(\sin^2 x+\cos^2 x)\nl2\sin^2 x-11\sin x○cos x+5\cos^2 x=0$

teď můžeš celou rovnici vydělit $\cos^2 x$ , protože kdyby pro x platilo, že je $\cos x=0$ , muselo by platit, že $2\sin^2 x=0\Rightarrow \sin x=0$ , ale protože pro žádné reálné číslo x neplatí současně cos x=0 a sin x=0, platí, že $\cos x\ne 0$

Zbytek zvládneš sám pomocí substituce. :)