Find constants $a$, $b$, $c$, $d$, and $e$ such that $\cos(4\theta)=a(\sin(\theta))^4 + b(\sin(\theta))^3 + c(\sin(\theta))^2 +d\sin(\theta))+e$ for all angles $\theta$. In other words, write $\cos(4\theta)$ as a polynomial in $\sin \theta$. How am I supposed to solve this problem?
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1$40$ should probably be $4\theta$ – Empy2 Feb 25 '24 at 16:56
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Indeed! If not, a solution is $a=b=c=d=0$, $e=\cos(40)$ ;-) – Anne Bauval Feb 25 '24 at 16:57
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Joking aside, please look at Quick beginner guide for asking a well-received question and avoid "no clue" questions: edit your post to show some work. – Anne Bauval Feb 25 '24 at 17:00