Mathematics, 28.01.2020 16:54 beeboppity
Write as an algebraic expression in terms of u: cot(cos^-1u)
Answers: 2
![\bf cot[cos^{-1}(u)]\\\\ -----------------------------\\\\ \textit{well, if }cos^{-1}(u)\textit{ give us an angle of say }\theta \\\\\\ \textit{that simply means that }cos(\theta)=u\iff cos(\theta)=\cfrac{u}{1}\\\\ -----------------------------\\\\ cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad cos(\theta)=\cfrac{u}{1}\cfrac{\leftarrow adjacent=a}{\leftarrow hypotenuse=c} \\\\\\](/tpl/images/0477/6104/59604.png)
![\bf \textit{let's find the value of "b", or the opposite side} \\\\\\ \textit{using the pythagorean theorem} \\\\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b\implies \sqrt{1^2-u^2}=b\\\\\\ \sqrt{1-u^2}=b\\\\ -----------------------------\\\\ thus \qquad cot[cos^{-1}(u)]\implies cot(\theta)\implies cot(\theta)=\cfrac{adjacent}{opposite} \\\\\\ cot(\theta)=\cfrac{u}{\sqrt{1-u^2}}](/tpl/images/0477/6104/8adf6.png)
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