elementry linear equation: using De Moivre's theorem,express cos4 theter and sin theter in terms of sines and cosines of multiples of theter

Question

dumbcow · Answer

$$\cos(4\theta)+i \sin(4\theta) = (\cos \theta+i \sin \theta)^{4}$$
is this what you mean?

anonymous · Answer

@Lesco , is it?

anonymous · Answer

yes, thank you so much.how can i determine the sixth roots of 8 as well as of -8.

dumbcow · Answer

$$x = \sqrt[6]{\pm 8}$$
$$x^{6}  \pm 8 = 0$$
Factor using sum/difference of cubes
$$(x^{2} \pm 2)(x^{4} \mp 2x^{2}+4)=0$$
From here you can solve for 2 roots from 1st term
for 2nd term, use quadratic formula

dumbcow · Answer

i think you can factor that further but i can't think of it at the moment

anonymous · Answer

thank you very much dumbcow, its been hard for to complete these questions, I'm new in linear equations ,i need help ..can you assist me with my assignment?

dumbcow · Answer

yes, i can help with questions you post