Question

find the exact value sin(arcsec 3x)

Answer 1

let \[\theta=arcsec3x\]
\[\sec \theta=3x\]
then draw a right traingle .. secant is r/x so we have r=3x x=1
and x^2+y^2=r^2
1+y^2=9x^2
y=sqrt(9x^2-1)

so we have r=3x. x=1, y= sqrt(9x^2-1)

sin is y/r

therefore sin(arcsec3x)=sqrt(9x^2-1)/3x