## anonymous 5 years ago Write the expression sin(tan^-1)x) as an algebraic expression in x (without trig or inverse trig functions). A. (sqrt (1+x^2))/ (x) B. (1) / (sqrt (1+x^2)) C. (x) / (sqrt (1-x^2)) D. (x) / (sqrt (1+x^2)) E. (1) / (sqrt (1-x^2))

1. anonymous

make a triangle... the ans will be obvious. it is opp/hyp so it is x/(x^2+1)

2. anonymous

Ah a triangle! Thank you!

3. anonymous

yes a triangle. label "opposite" side x and adjacent side 1 since the tangent is x = x/1 use pythatoras to find the hypotenuse which will be $\sqrt{1+x^2}$

4. anonymous

then $sin(tan^{-1}(x))=\frac{x}{\sqrt{1+x^2}}$

5. anonymous

that being opposite over hypotenuse

6. anonymous

and by the same triangle $cos(tan^{-1}(x))=\frac{1}{\sqrt{1+x^2}}$