Question

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))

Answer 1

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

Answer 2

Ah a triangle! Thank you!

Answer 3

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
\[\sqrt{1+x^2}\]

Answer 4

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

Answer 5

that being opposite over hypotenuse

Answer 6

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