QuestionConvert the trigonometric expression $\sin \left(\tan ^{-1} u\right)$ to an algebraic form in $u$ .

Studdy Solution

STEP 1

Assumptions1. We are given a trigonometric expression $\sin \left(\tan ^{-1} u\right)$ . We are asked to write this expression as an algebraic expression in $u$ .

STEP 2

We can use the identity $\sin(\tan^{-1}x) = \frac{x}{\sqrt{1+x^2}}$ to simplify the expression. This identity comes from the right triangle definition of sine and tangent.

STEP 3

Substitute $u$ into the identity to get the algebraic expression in $u$ .
$\sin \left(\tan ^{-1} u\right) = \frac{u}{\sqrt{1+u^2}}$ So, the algebraic expression of $\sin \left(\tan ^{-1} u\right)$ in $u$ is $\frac{u}{\sqrt{1+u^2}}$ .

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