given that cis 3Ө = (cos^{3 }Ө - 3 cos Ө sin^{2 }Ө) + i (3 cos^{2 }Ө sin Ө - sin^{3 }Ө) it follows that cos 3Ө is equal to?
I really don't know how to do this, any help would be appreciated :/
given that cis 3Ө = (cos^{3 }Ө - 3 cos Ө sin^{2 }Ө) + i (3 cos^{2 }Ө sin Ө - sin^{3 }Ө) it follows that cos 3Ө is equal to?
I really don't know how to do this, any help would be appreciated :/
cis$\displaystyle 3\theta$ is shorthand for $\displaystyle \cos 3\theta + i\sin 3\theta$ so your first step is to equate reals and imaginaries and to see what that leads to.
I did try cos 3Ө = cos^3 Ө - 3 cos Ө sin^2 Ө
but I don't know what to do after that point. I went to this site Table of Trigonometric Identities for trig identities and subbed them in, but to no avail.
oh my, I think I may have actually got it thanks to that ^
but not sure if my working is legit or not.
One question,
is there an equivalent for cos^3 (Ө), or any with powers?
And, would something like cos 3Ө = 3 cos Ө?