Chapter 12.9, Problem 4CYU

To determine

To find the value of the given expression round to the nearest hundredth.

Answer to Problem 4CYU

  $\frac{3}{5}$

Explanation of Solution

Given: $\cos \left(\mathrm{Arcsin}\frac{4}{5}\right)$

Calculation: Let $\begin{array}{l}\mathrm{Arcsin}\frac{4}{5}=x\\ \Rightarrow \frac{4}{5}=\sin x=\frac{\text{perpendicular}\left(p\right)}{\text{hypotenuse}\left(h\right)}\end{array}$

Now, let p = 4y and h = 5y, So

  $\begin{array}{l}b=\sqrt{h^2-p^2}\\ \Rightarrow b=\sqrt{{\left(5y\right)}^2-{\left(4y\right)}^2}\\ \Rightarrow b=\sqrt{25y^2-16y^2}\\ \Rightarrow b=\sqrt{9y^2}\\ \Rightarrow b=3y\\ \cos \left(\mathrm{Arcsin}\frac{4}{5}\right)\\ =\cos x\\ =\frac{b}{h}\\ =\frac{3y}{5y}\\ =\frac{3}{5}\end{array}$

Thus, obtained value is equal to the given expression.