rownania trygonometryczne

[mart1na]

1. \(\displaystyle{ sin^{2}x+\frac{1}{4}=sinx}\)

2. \(\displaystyle{ 3cosx+1=cos2x}\)

3. \(\displaystyle{ cos2x+\frac{3}{4}=cos^{2}x}\)

4. \(\displaystyle{ tg^{2}(x+\frac{\pi}{4})-3=0}\)

5. \(\displaystyle{ 4cos^{2}(\frac{2}{3}\pi -x)-3=0}\)

6. \(\displaystyle{ ctg^{3}\frac{x}{2}-ctg\frac{x}{2}=0}\)

7. \(\displaystyle{ 2sin^{2}x+\sqrt{2}sinx=2}\)

8. \(\displaystyle{ cos2x-3cosx+2=0}\)

9. \(\displaystyle{ cos2x+5sinx=4}\)

10. \(\displaystyle{ -cos2x-5sinx+5=\frac{1}{sinx}}\)

11. \(\displaystyle{ cos^{2}x=cosx cos2x}\)

bylabym wdzieczna za pomoc ;]

[szablewskil]

3)\(\displaystyle{ cos2x+\frac{3}{4}=cos^{2}x 2cos^{2}x- 1 + \frac{3}{4}=cos^{2}x cos^{2}x= \frac{1}{4} x=k*\pi+ \frac{\pi}{3} x=k*\pi+\frac{2\pi}{3}}\)

[tkrass]

1.
\(\displaystyle{ sin^{2}x+\frac{1}{4}=sinx}\)
\(\displaystyle{ sin^{2}x-sinx+\frac{1}{4}=0}\)
\(\displaystyle{ sinx=t}\)
\(\displaystyle{ t ^{2} -t+ \frac{1}{4} =0}\)
\(\displaystyle{ \Delta=1-1=0}\)
\(\displaystyle{ t= \frac{-(-1)}{2 1} = \frac{1}{2}}\)
\(\displaystyle{ sinx= \frac{1}{2}}\)