Free Printable Ponavljanje

1.

Koliko se rješenja trigonometrijske jednadžbe $3\cos2x+2\sin^2x=0$ nalazi u intervalu $\left[0,2\pi\right]$ ?

a)

Jedno

b)

Dva

c)

Tri

d)

Četiri

2.

Ako je $\cos x=0.6\$ i $x\in<\frac{3\pi}{2},\ 2\pi>$ , koliko je $\cos\left(x-\frac{\pi}{3}\right)$ ?

a)

$-0.4472$

b)

$-0.39282$

c)

$0.1$

d)

$0.5$

3.

Koliko rješenja ima jednadžba $2\cos\left(3x\right)+1=0$ na intervalu $\left[0,\ \pi\right]$ ?

a)

Jedno

b)

Dva

c)

Tri

d)

Četiri

4.

Koja od navedenih jednadžbi nema realnih rješenja?

a)

$\frac{x-3}{x}=0$

b)

$\sqrt[]{x-3}=0$

c)

$\sin x=-2$

d)

$\tan x=-2$

5.

Riješi jednadžbu $\tan x+\frac{4}{\tan x}=4$ .

a)

$x=1.1071+2k\pi,\ k\in Z$

b)

$x=\frac{\pi}{3}+k\pi,\ k\in Z$

c)

$x=1.1771+k\pi,\ k\in Z$

d)

$x=1.1071+k\pi,\ k\in Z$

6.

Riješi jednadžbu $4\cos x=\sin\left(\frac{5\pi}{6}-x\right)$ .

a)

$x=1.328+k\pi,\ k\in Z$

b)

$x=0.524+k\pi,\ k\in Z$

c)

$x=1.381+k\pi,\ k\in Z$

d)

$x=1.381+2k\pi,\ k\in Z$

7.

Riješi jednadžbu $\sqrt[]{3}\sin x-\cos x=0$ .

a)

$x=-\frac{\pi}{6}+2k\pi,\ k\in Z$

b)

$x=\frac{5\pi}{6}+k\pi,\ k\in Z$

c)

$x=\frac{\pi}{6}+2k\pi,\ k\in Z$

d)

$x=\frac{\pi}{6}+k\pi,\ k\in Z$

8.

Riješi sustav jednadžbi

$\sin\left(y-x\right)=\frac{1}{2}$

$2x-y=\frac{\pi}{3}$

a)

$\left(\frac{\pi}{2}+2k\pi,\ \frac{2\pi}{3}+2k\pi\right),\ k\in Z$ $\left(\frac{7\pi}{6}+2k\pi,\ \frac{5\pi}{6}+2k\pi\right),\ k\in Z$

b)

$\left(\frac{\pi}{2}+k\pi,\ \frac{2\pi}{3}+k\pi\right),\ k\in Z$ $\left(\frac{7\pi}{6}+k\pi,\ \frac{5\pi}{6}+k\pi\right),\ k\in Z$

c)

$\left(\frac{\pi}{2}+2k\pi,\ \frac{2\pi}{3}+4k\pi\right),\ k\in Z$ $\left(\frac{7\pi}{6}+2k\pi,\ \frac{5\pi}{6}+4k\pi\right),\ k\in Z$

9.

Za koje sve vrijednosti realnog broja $a$ jednadžba $\sin^3x\cdot\cos x+\sin x\cdot\cos^3x=\frac{3-a}{4}$ ima rješenja?

a)

$a\in\left[1,3\right]$

b)

$a\in\left[-5,-1\right]$

c)

$a\in\left[-1,5\right]$

d)

$a\in\left[1,5\right]$

10.

Odredi sva rješenja jednadžbe $\cos\left(x-\frac{\pi}{7}\right)=1$ .

a)

$x_1=\frac{\pi}{7}+2k\pi,\ k\in Z$ $x_2=-\frac{\pi}{7}+2k\pi,\ k\in Z$

b)

$x_1=\frac{\pi}{7}+k\pi,\ k\in Z$ $x_2=-\frac{\pi}{7}+k\pi,\ k\in Z$

c)

$x=\frac{\pi}{7}+2k\pi,\ k\in Z$

d)

$x=\frac{\pi}{7}+k\pi,\ k\in Z$

Ponavljanje

Total questions: 10

Worksheet time: 2hrs 40mins

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