Q. 11 - Precalculus Enhanced with Graphing Utilities

Question

11. Find the exact value of $\tan \left(\frac{\mathrm{\pi }}{4}\right)- 3\cos \left(\frac{\mathrm{\pi }}{6}\right)+\frac{1}{\sin \left({\displaystyle \frac{\mathrm{\pi }}{6}}\right)}$

Step-by-Step Solution

Answer

The exact value of given function is: $0.40192$

Step 1. Given Information

$\tan \left(\frac{\mathrm{\pi }}{4}\right)-3\cos \left(\frac{\mathrm{\pi }}{6}\right)+\frac{1}{\sin \left({\displaystyle \frac{\mathrm{\pi }}{6}}\right)}$

We know that 

$\tan \left(\frac{\mathrm{\pi }}{4}\right)= 1$

$\cos \left(\frac{\mathrm{\pi }}{6}\right)= 0.866$

$\frac{1}{\sin \left({\displaystyle \frac{\mathrm{\pi }}{6}}\right)}= 2$

Step 2 .calculating all the values

$1-\left( 3\times 0.866\right)+2$=$0.4019$