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I need help with this, struggling to solveIt’s from my ACT prep guide

I need help with this, struggling to solveIt’s from my ACT prep guide-example-1
User Bitmagier
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1 Answer

3 votes

Given the expression:


(\tan(-(2\pi)/(3)))/(\sin((7\pi)/(4)))-\sec (-\pi)

We will find each trigonometric function the substitute into the expression

We will find each value with the help of the reference angle


\tan (-(2\pi)/(3))=\tan ((4\pi)/(3))=\tan (\pi+(\pi)/(3))=\tan ((\pi)/(3))=\sqrt[]{3}
\sin ((7\pi)/(4))=\sin (2\pi-(\pi)/(4))=-\sin ((\pi)/(4))=-\frac{1}{\sqrt[]{2}}
\sec (-\pi)=\sec (-\pi+2\pi)=\sec \pi=-1

Substitute with the recent values:


\begin{gathered} (\tan(-(2\pi)/(3)))/(\sin((7\pi)/(4)))-\sec (-\pi)=(\sqrt[]{3}/-\frac{1}{\sqrt[]{2}})-(-1) \\ \\ =(\sqrt[]{3}\cdot(-\sqrt[]{2}))+1=-\sqrt[]{6}+1 \end{gathered}

So, the answer will be:


-\sqrt[]{6}+1

User Sandeep Manne
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