Question

Make the substitution =5sin to simplify the expression √25−2

Answer 1

ANSWER:

5 cos

STEP-BY-STEP EXPLANATION:

We have the following expression:

$\sqrt{25-x^2}$

We substitute when x = 5 sin and get the following:

$\begin{gathered} \sqrt{25-\left(5\sin\left(\theta\right)\right)^2} \\ \\ \sqrt{25-5^2\sin^2\left(\theta\right)} \\ \\ 25-5^2\sin^2(\theta)=25\cdot\:1-25\sin^2\left(\theta\right)=25\left(1-\sin^2\left(\theta\right)\right) \\ \\ \sqrt{25\left(1-\sin^2\left(\theta\right)\right)}=\sqrt{25}\cdot\sqrt{1-\sin^2\left(\theta\right)}=5\sqrt{\cos^2\left(\theta\right)}=5\cos\theta \\ \end{gathered}$