Cyklometrické funkcie
Úloha 1
Priraď správnu funkčnú hodnotu:
A | B | C | D | E | F | G | ||
{\pi \over 6} | {\pi \over 2} | -{\pi \over 2} | {\pi \over 3} | 0 | {\pi \over 4} | \pi | ||
a) {\rm arctg}\: 1 | ||||||||
b) {\rm arcsin}\: -1 | ||||||||
c) {\rm arcsin}\: \large {1 \over 2} | ||||||||
d) {\rm arccos}\: \large {1 \over 2} | ||||||||
e) {\rm arccotg}\: 0 | ||||||||
f) {\rm arctg}\: 0 | ||||||||
h) {\rm arccos}\: -1 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 132 |
Úloha 2
Zisti predpis funkcie, ktorá je vykreslená na obrázku!
a)
![](images/priklady/asin1.png)
y = -\arccos x + 1
y = \arccos x + 1 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 146
b)
![](images/priklady/atan1.png)
y = {\rm arctg}\: x + 1
y = 2{\rm arctg}\: x + 1 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 160
c)
![](images/priklady/acos1.png)
y = \frac {1}{2} {\rm arccos}\: x - 1
y = {\rm arccos}\: x - 1 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 173
d)
![](images/priklady/acot1.png)
y = 2{\rm arccotg}\: x - 2
y = 2{\rm arctg}\: x - 2
Úloha 3
Zisti, ktorý graf odpovedá zadanému predpisu funkcie!
a)
f(x) = 2{\rm arcsin}\: x Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 194 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 195 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 196
![](images/priklady/asin2a.png)
![](images/priklady/asin2b.png)
![](images/priklady/asin2c.png)
b)
f(x) = {\rm arccos}\: x - 1 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 208 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 209 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 210
![](images/priklady/acos2a.png)
![](images/priklady/acos2b.png)
![](images/priklady/acos2c.png)
c)
f(x) = -2{\rm arctg}\: x Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 222 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 223 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 224
![](images/priklady/atan2a.png)
![](images/priklady/atan2b.png)
![](images/priklady/atan2c.png)
d)
f(x) = {\rm arccotg}\: x -1 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 236 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 237 Notice: Undefined variable: prefix in /srv/beegfs/web/web/kdm/diplomky/matus_kepic_dp/gon_rovnice_nerovnice/include/testy.cyklo.inc on line 238
![](images/priklady/acot2a.png)
![](images/priklady/acot2c.png)
![](images/priklady/acot2b.png)