Grafy goniometrických funkcií I

Project ID: 
6000000036
Accepted: 
Typ: 
Layout: 
Question: 
K predpisu funkcie priraďte jej graf:
Question 1 Image: 
Answer 1: 
$f(x)=\sin (3x)$
Question 2 Image: 
Answer 2: 
$f(x)=\cos \!\left (2x+\frac {\pi }2\right )$
Question 3 Image: 
Answer 3: 
$f(x)=-\sin (2x+\pi )$
Question 4 Image: 
Answer 4: 
$f(x)=-\sin \!\left (x-\frac {\pi }2\right )$
Answer 5: 

$f(x)=-\sin (3x)$

Answer 6: 
$f(x)=-\sin \!\left (x+\frac {\pi }2\right )$
Tex: 
% tiket 32577 \NastavOD{3} \NastavOT{3} \otazka{\obrA}{$f(x)=\sin(3x)$} \otazka{\obrB}{$f(x)=\cos\!\left(2x+\frac{\pi}2\right)$} \otazka{\obrC}{$f(x)=-\sin(2x+\pi)$} \otazka{\obrD}{$f(x)=-\sin\!\left(x-\frac{\pi}2\right)$} \fake{$f(x)=-\sin(3x)$} \fake{$f(x)=-\sin\!\left(x+\frac{\pi}2\right)$} \def\delka{0.35cm} \def\PI{3.14} \def\obrA{ \obrMsr[x=\delka,y=2*\delka]{-3*\PI}{3*\PI}{-3}{3} { \footnotesize \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisY[left]{-2,-1,1,2} \obrZnackyX{-2*\PI,-\PI,\PI,2*\PI} \draw[gray!30,thin] (-2*\PI,-3) -- (-2*\PI,3); \draw[gray!30,thin] (-\PI,-3) -- (-\PI,3); \draw[gray!30,thin] (\PI,-3) -- (\PI,3); \draw[gray!30,thin] (2*\PI,-3) -- (2*\PI,3); \draw[gray!30,thin] (-3*\PI,-2) -- (3*\PI,-2); \draw[gray!30,thin] (-3*\PI,-1) -- (3*\PI,-1); \draw[gray!30,thin] (-3*\PI,1) -- (3*\PI,1); \draw[gray!30,thin] (-3*\PI,2) -- (3*\PI,2); \draw (-2*\PI,0) node [below]{$-2\pi$}; \draw (-\PI,0) node [below]{$-\pi$}; \draw (\PI,0) node [below]{$\pi$}; \draw (2*\PI,0) node [below]{$2\pi$}; \draw[thick] (-18*\PI/6,0) sin (-17*\PI/6,-1) cos (-16*\PI/6,0) sin (-15*\PI/6,1) cos (-14*\PI/6,0) sin (-13*\PI/6,-1) cos (-12*\PI/6,0) sin (-11*\PI/6,1) cos (-10*\PI/6,0) sin (-9*\PI/6,-1) cos (-8*\PI/6,0) sin (-7*\PI/6,1) cos (-6*\PI/6,0) sin (-5*\PI/6,-1) cos (-4*\PI/6,0) sin (-3*\PI/6,1) cos (-2*\PI/6,0) sin (-\PI/6,-1) cos (0,0) sin (\PI/6,1) cos (2*\PI/6,0) sin (3*\PI/6,-1) cos (4*\PI/6,0) sin (5*\PI/6,1) cos (6*\PI/6,0) sin (7*\PI/6,-1) cos (8*\PI/6,0) sin (9*\PI/6,1) cos (10*\PI/6,0) sin (11*\PI/6,-1) cos (12*\PI/6,0) sin (13*\PI/6,1) cos (14*\PI/6,0) sin (15*\PI/6,-1) cos (16*\PI/6,0) sin (17*\PI/6,1) cos (18*\PI/6,0); } } \def\obrB{ \obrMsr[x=\delka,y=2*\delka]{-3*\PI}{3*\PI}{-3}{3} { \footnotesize \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisY[left]{-2,-1,1,2} \obrZnackyX{-2*\PI,-\PI,\PI,2*\PI} \draw[gray!30,thin] (-2*\PI,-3) -- (-2*\PI,3); \draw[gray!30,thin] (-\PI,-3) -- (-\PI,3); \draw[gray!30,thin] (\PI,-3) -- (\PI,3); \draw[gray!30,thin] (2*\PI,-3) -- (2*\PI,3); \draw[gray!30,thin] (-3*\PI,-2) -- (3*\PI,-2); \draw[gray!30,thin] (-3*\PI,-1) -- (3*\PI,-1); \draw[gray!30,thin] (-3*\PI,1) -- (3*\PI,1); \draw[gray!30,thin] (-3*\PI,2) -- (3*\PI,2); \draw (-2*\PI,0) node [below]{$-2\pi$}; \draw (-\PI,0) node [below]{$-\pi$}; \draw (\PI,0) node [below]{$\pi$}; \draw (2*\PI,0) node [below]{$2\pi$}; \draw[thick] (-12*\PI/4,0) sin (-11*\PI/4,-1) cos (-10*\PI/4,0) sin (-9*\PI/4,1) cos (-8*\PI/4,0) sin (-7*\PI/4,-1) cos (-6*\PI/4,0) sin (-5*\PI/4,1) cos (-4*\PI/4,0) sin (-3*\PI/4,-1) cos (-2*\PI/4,0) sin (-\PI/4,1) cos (0,0) sin (\PI/4,-1) cos (2*\PI/4,0) sin (3*\PI/4,1) cos (4*\PI/4,0) sin (5*\PI/4,-1) cos (6*\PI/4,0) sin (7*\PI/4,1) cos (8*\PI/4,0) sin (9*\PI/4,-1) cos (10*\PI/4,0) sin (11*\PI/4,1) cos (12*\PI/4,0); } } \def\obrC{ \obrMsr[x=\delka,y=2*\delka]{-3*\PI}{3*\PI}{-3}{3} { \footnotesize \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisY[left]{-2,-1,1,2} \obrZnackyX{-2*\PI,-\PI,\PI,2*\PI} \draw[gray!30,thin] (-2*\PI,-3) -- (-2*\PI,3); \draw[gray!30,thin] (-\PI,-3) -- (-\PI,3); \draw[gray!30,thin] (\PI,-3) -- (\PI,3); \draw[gray!30,thin] (2*\PI,-3) -- (2*\PI,3); \draw[gray!30,thin] (-3*\PI,-2) -- (3*\PI,-2); \draw[gray!30,thin] (-3*\PI,-1) -- (3*\PI,-1); \draw[gray!30,thin] (-3*\PI,1) -- (3*\PI,1); \draw[gray!30,thin] (-3*\PI,2) -- (3*\PI,2); \draw (-2*\PI,0) node [below]{$-2\pi$}; \draw (-\PI,0) node [below]{$-\pi$}; \draw (\PI,0) node [below]{$\pi$}; \draw (2*\PI,0) node [below]{$2\pi$}; \draw[thick] (-12*\PI/4,0) sin (-11*\PI/4,1) cos (-10*\PI/4,0) sin (-9*\PI/4,-1) cos (-8*\PI/4,0) sin (-7*\PI/4,1) cos (-6*\PI/4,0) sin (-5*\PI/4,-1) cos (-4*\PI/4,0) sin (-3*\PI/4,1) cos (-2*\PI/4,0) sin (-\PI/4,-1) cos (0,0) sin (\PI/4,1) cos (2*\PI/4,0) sin (3*\PI/4,-1) cos (4*\PI/4,0) sin (5*\PI/4,1) cos (6*\PI/4,0) sin (7*\PI/4,-1) cos (8*\PI/4,0) sin (9*\PI/4,1) cos (10*\PI/4,0) sin (11*\PI/4,-1) cos (12*\PI/4,0); } } \def\obrD{ \obrMsr[x=\delka,y=2*\delka]{-3*\PI}{3*\PI}{-3}{3} { \footnotesize \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisY[left]{-2,-1,1,2} \obrZnackyX{-2*\PI,-\PI,\PI,2*\PI} \draw[gray!30,thin] (-2*\PI,-3) -- (-2*\PI,3); \draw[gray!30,thin] (-\PI,-3) -- (-\PI,3); \draw[gray!30,thin] (\PI,-3) -- (\PI,3); \draw[gray!30,thin] (2*\PI,-3) -- (2*\PI,3); \draw[gray!30,thin] (-3*\PI,-2) -- (3*\PI,-2); \draw[gray!30,thin] (-3*\PI,-1) -- (3*\PI,-1); \draw[gray!30,thin] (-3*\PI,1) -- (3*\PI,1); \draw[gray!30,thin] (-3*\PI,2) -- (3*\PI,2); \draw (-2*\PI,0) node [below]{$-2\pi$}; \draw (-\PI,0) node [below]{$-\pi$}; \draw (\PI,0) node [below]{$\pi$}; \draw (2*\PI,0) node [below]{$2\pi$}; \draw[thick] (-6*\PI/2,-1) cos (-5*\PI/2,0) sin (-4*\PI/2,1) cos (-3*\PI/2,0) sin (-2*\PI/2,-1) cos (-\PI/2,0) sin (0,1) cos (\PI/2,0) sin (2*\PI/2,-1) cos (3*\PI/2,0) sin (4*\PI/2,1) cos (5*\PI/2,0) sin (6*\PI/2,-1) ; } }