## Mandy_Nakamoto Group Title Using de Moivre’s theorem, express cos 6θ and sin 6θ in powers of cos θ and sin θ. Do i have to use binomial expansion?? 2 years ago 2 years ago

1. dumbcow Group Title

yes i believe you do have to use binomial expansion $\cos(6 \theta)+\sin(6 \theta) = (\cos \theta +\sin \theta)^{6}$

2. Soham051994 Group Title

but it says using demoivre..so binomial isnt needed i think'

3. Mandy_Nakamoto Group Title

isn't needed?? i don't understand..

4. dumbcow Group Title

wait i forgot the "i" the equality only holds if dealing with complex numbers $\cos(6 \theta)+i \sin(6 \theta) = (\cos \theta +i \sin \theta)^{6}$

5. Soham051994 Group Title

right

6. Mandy_Nakamoto Group Title

i always did like what @dumbcow did.. is there other alternative??

7. Soham051994 Group Title

if it says without demoivre,,then there are other wayss

8. dumbcow Group Title

$=\cos^{6}+6i \cos^{5}\sin-15\cos^{4}\sin^{2}-20i \cos^{3}\sin^{3}+15\cos^{2}\sin^{4}+6i \cos \sin^{5}-\sin^{6}$

9. Soham051994 Group Title

i think you dont need the expansion,as it said find in terms of powers of costheta

10. Soham051994 Group Title

find cos6theta in terms of costheta and sin6theta in terms of sintheta,are these separate or same question?

11. Mandy_Nakamoto Group Title

find cos6θ and sin 6θ in powers of cos θ and sin θ.. the same.. i think i have to use the binomial..

12. Mandy_Nakamoto Group Title

so i just have to expand it and that's it?? Do i have to separate it between the real and the imaginary in the end??

13. Soham051994 Group Title

the question is find cos6theta and sin6theta , it indicates they are different sums........ it is "and", why take it as +

14. dumbcow Group Title

soham, because de'moivres theorem is mentioned i think it was implied mandy, yes i believe you would have to separate real and imaginary coefficients

15. Mandy_Nakamoto Group Title

Thanks a lot!! Im not lost anymore.. ^^

16. Soham051994 Group Title

right