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Ecuatii trigonometrice

Total questions: 10

Worksheet time: 13mins

Name
Class
Date
1.

Ecuatia cosx=1 are soluțiile 

a)

±π2+kπ,k∈Z\pm\frac{\pi}{2}+k\pi,k\in Z

b)

±πk,k∈Z\pm\pi k,k\in Z

c)

2kπ,k∈Z2k\pi,k\in Z

d)

±π4+2kπ,k∈Z\pm\frac{\pi}{4}+2k\pi,k\in Z

2.

Ecuatia sinx= - 2 are solutiile

a)

(−1)karcsin⁡(−2)±kπ,k∈Z\left(-1\right)^k\arcsin\left(-2\right)\pm k\pi,k\in Z

b)

n-are solutii

c)

±2kπ,k∈Z\pm2k\pi,k\in Z

d)

π2+2kπ,k∈Z\frac{\pi}{2}+2k\pi,k\in Z

3.

DVA al ecuaței  tgx=2 este:

a)

R≠{π2+kπ,k∈Z}R\ne\left\{\frac{\pi}{2}+k\pi,k\in Z\right\}

b)

{π2+kπ,k∈Z}\left\{\frac{\pi}{2}+k\pi,k\in Z\right\}

c)

R≠{kπ,k∈Z}R\ne\left\{k\pi,k\in Z\right\}

d)

{πk,k∈Z}\left\{\pi k,k\in Z\right\}

4.

 2sin⁡2x+5sin⁡x=3 este ecuatie:2\sin^2x+5\sin x=3\ este\ ecuatie:  

a)

Trigonometrica fundamentala

b)

Trigonometrica omogena

c)

Trigonometrica reductibila la ecuatii algebrica

d)

Nu este ecuatie trigonometrica

5.

 Ecuatia 2sin⁡x=0 are solutiileEcuatia\ 2\sin x=0\ are\ solutiile  

a)

 {±π2+kπ,k∈Z}\left\{\pm\frac{\pi}{2}+k\pi,k\in Z\right\}  

b)

 RR  

c)

 {kπ,k∈Z}\left\{k\pi,k\in Z\right\}  

d)

Nu are solutii

6.

 Ecuația ctg⁡x=4 are soluțiile:Ecuația\ \operatorname{ctg}x=4\ are\ soluțiile:  

a)

 {4kπ,k∈Z}\left\{4k\pi,k\in Z\right\}  

b)

 {arcctg⁡4 +kπ,k∈Z}\left\{\operatorname{arcctg}4\ +k\pi,k\in Z\right\}  

c)

 {arctg⁡4 +kπ,k∈Z}\left\{ar\operatorname{ctg}4\ +k\pi,k\in Z\right\}  

d)

Nu are solutii

7.

Rezolvă ecuația  2sin⁡(2x−3)=2,apoi bifeaza2\sin\left(2x-3\right)=\sqrt{2},apoi\ bifeaza  

a)

 {π4+kπ,k∈Z}\left\{\frac{\pi}{4}+k\pi,k\in Z\right\}  

b)

 {(−1)k π8+32+kπ2,k∈Z}\left\{\left(-1\right)^k\ \frac{\pi}{8}+\frac{3}{2}+\frac{k\pi}{2},k\in Z\right\}  

c)

 {(−1)k π3+kπ2,k∈Z}\left\{\left(-1\right)^k\ \frac{\pi}{3}+\frac{k\pi}{2},k\in Z\right\}  

d)

N-are solutii

8.

Rezolvă cos⁡2x+2cos⁡x+1=0 \cos^2x+2\cos x+1=0\  

apoi bifează răspunsul corect 

a)

 {±kπ,k∈Z}\left\{\pm k\pi,k\in Z\right\}  

b)

 {π+2kπ,k∈Z}\left\{\pi+2k\pi,k\in Z\right\}  

c)

 {(−1)kπ+kπ,k∈Z}\left\{\left(-1\right)^k\pi+k\pi,k\in Z\right\}  

d)

 {±2kπ,k∈Z}\left\{\pm2k\pi,k\in Z\right\}  

9.

Ecuatia de forma   cos⁡2x+5cos⁡xsin⁡x−sin⁡2x=0 \cos^2x+5\cos x\sin x-\sin^2x=0\   


este ecuație:

a)

Trigonometrica fundamentala

b)

Trigonometrica omogena

c)

Trifonometrica reductibila la ecuatii algebrice

d)

Nu este ecuatie trigonometrica

10.

Rezolvă ecuația cos⁡2x−2sin⁡xcos⁡x=1 \cos^2x-2\sin x\cos x=1\   apoi 


bifează răspunsul corect

a)

 {±kπ,k∈Z}\left\{\pm k\pi,k\in Z\right\}  

b)

 {±π3+2kπ,k∈Z}∪{nπ,n∈Z}\left\{\pm\frac{\pi}{3}+2k\pi,k\in Z\right\}\cup\left\{n\pi,n\in Z\right\}  

c)

 {π2+2kπ,k∈Z}∪{π3+nπ,n∈Z}\left\{\frac{\pi}{2}+2k\pi,k\in Z\right\}\cup\left\{\frac{\pi}{3}+n\pi,n\in Z\right\}  

d)

N-are solutii