Question

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

Answer 1

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`