Q. 11 - Precalculus Enhanced with Graphing Utilities

Question

find the exact value of the expression  

$\sin \left(\frac{\mathrm{\pi }}{2}\right)-\tan \left(\frac{19\mathrm{\pi }}{4}\right)$

Step-by-Step Solution

Answer

$\sin \left(\frac{\mathrm{\pi }}{2}\right)-\tan \left(\frac{19\mathrm{\pi }}{4}\right)=2$

Step 1. Rewriting the expression

$$\begin{gathered} we know that \\ \tan (5\mathrm{\pi }-\mathrm{x})=-\mathrm{tanx} \\ \mathrm{So} \mathrm{given} \mathrm{expression} \mathrm{can} \mathrm{be} \mathrm{written} \mathrm{as} \\ \sin \left(\frac{\mathrm{\pi }}{2}\right)-\tan (5\mathrm{\pi }-\frac{\mathrm{\pi }}{4}) \\ \sin \left(\frac{\mathrm{\pi }}{2}\right)+\tan \left(\frac{\mathrm{\pi }}{4}\right) \end{gathered}$$

Step 2. Calculations

Now our expression becomes $$\begin{gathered} \sin \left(\frac{\mathrm{\pi }}{2}\right)+\tan \left(\frac{\mathrm{\pi }}{4}\right) \\ 1+1=2 \end{gathered}$$