Question

I need help with this, struggling It’s from my Act Prep guide 21’-22’

Answer 1

We need to evaluate the expression:

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

So, let's find the value of each trigonometric function separately, and then we can evaluate the whole expression.

We have:

`\tan (-(2\pi)/(3))=\tan ((\pi)/(3))=\sqrt[]{3}`

Also:

`\sin ((7\pi)/(4))=-\sin ((\pi)/(4))=-\frac{1}{\sqrt[]{2}}`

And:

`\begin{gathered} \sec (-\pi)=(1)/(\cos(-\pi))=(1)/(\cos \pi)=(1)/(-1) \\ \\ -\sec (-\pi)=1 \end{gathered}`

Therefore, the value of the whole expression is:

`\begin{gathered} \frac{\sqrt[]{3}}{-\frac{1}{\sqrt[]{2}}}+1 \\ \\ \sqrt[]{3}\cdot(-\sqrt[]{2})+1 \\ \\ -\sqrt[]{6}+1 \\ \\ 1-\sqrt[]{6} \end{gathered}`

Thus, the answer is:

`1-\sqrt[]{6}`