Question 1190009

given:

{{{sin(A)=2/3 }}}and {{{A}}} is obtuse

if {{{sin(A)=2/3 }}} than

{{{A=sin^-1(2/3)}}}

{{{A=138.19}}}° (obtuse)


if

{{{sin(A)=2/3 }}}=> {{{opp/hyp=2/3 }}}=> {{{opp=2}}}, {{{hyp=3}}}

than {{{adj=sqrt(3^2-2^2)=sqrt(5)}}}



1)

{{{cos(A)=sqrt(5)/3}}}


2)

{{{sin(2A)=2 sin(A) cos(A)}}}


{{{sin(2A)=2(2/3) (sqrt(5)/3)}}}


{{{sin(2A)=(4sqrt(5))/9}}}



3) 

{{{tan(2A)=(2sin(A)cos(A))/(cos^2(A) - sin^2(A))}}}


{{{tan(2A)=(2(2/3)(sqrt(5)/3))/((sqrt(5)/3)^2 - (2/3)^2)}}}


{{{tan(2A)=((4sqrt(5))/9)/(1/9)}}}


{{{tan(2A)=4sqrt(5)}}}