Q47. - Algebra 2

Question

Solve the equation $Arccos\left(\frac{\sqrt{2}}{2}\right)=x$.

Step-by-Step Solution

Answer

The solution for the equation is $x=\frac{\pi }{4}$.

Step 1. Write down the given equation.

The given equation is $arccos\left(\frac{\sqrt{2}}{2}\right)=x$.

Step 2. Simplify the equation.

The given equation $arccos\left(\frac{2}{\sqrt{2}}\right)=y$ is solved as:

$\begin{array}{c}arccos\left(\frac{\sqrt{2}}{2}\right)=x\mathrm{....}\left(\text{Given}\right)\\ x={\cos }^{-1}\left(\frac{1}{\sqrt{2}}\right)\\ \cos x=\frac{1}{\sqrt{2}}\\ x=\frac{\pi }{4}\end{array}$

Step 3. Conclusion.

The solution for the given equation is $x=\frac{\pi }{4}$.