Question 1155697

If {{{sec(A) = sqrt(65)}}}, and {{{A}}} is in Quadrant 1, 

find {{{sin(2A)}}} and {{{sin(A/2)}}}


use identity:

{{{sec (A)=1/cos(A)}}}


{{{cos(A)=1/sec(A)}}}......plug in given


{{{cos(A)=1/sqrt(65)}}}


use identity:

{{{sin^2(A)+cos^2(A)=1}}}


{{{sin^2(A)=1-cos^2(A)}}}..........{{{cos^2(A)=(1/sqrt(65))^2=1/65}}}


{{{sin^2(A)=1-1/65}}}


{{{sin^2(A)=64/65}}}


{{{sin(A)=sqrt(64/65)}}}


{{{sin(A)=sqrt(64)/sqrt(65)}}}


{{{sin(A)=8/sqrt(65)}}}


use identity:

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


{{{sin(2A) =2(8/sqrt(65))*(1/sqrt(65))}}}


{{{sin(2A) =16/(sqrt(65)*sqrt(65))}}}


{{{sin(2A) =16/65}}}


use identity:

{{{sin(A/2)=2 sin(A/4) *cos(A/4)}}}


{{{sin(A/2)=2((8/sqrt(65))/4)*((1/sqrt(65))/4)}}}


{{{sin(A/2)=2(2/sqrt(65))*(1/(4sqrt(65)))}}}


{{{sin(A/2)= (4/sqrt(65))*(1/(4sqrt(65)))}}}


{{{sin(A/2)= 1/65}}}