Question 867967
Identity, double angle:  {{{sine(2*theta)=2*sin(theta)cos(theta)}}}
Use also the identity {{{cos^2(theta)+sin^2(theta)=1}}} which gives you {{{cos(theta)=sqrt(1-sin^2(theta))}}}.


sine is {{{3/8}}} for {{{theta}}}, you want as the double angle, {{{sin(2*theta)=2(3/8)*cos(theta)}}}
{{{highlight(sin(2*theta)=2(3/8)*sqrt(1-(3/8)^2))}}}----only needing computation to finish into final value simplified.


Decimal approximation, 0.695, but I suggest working through into simplest radical form, FIRST.



Note that for {{{sin(theta)=3/8}}}, this is an angle of about 22 degrees.   {{{2*theta}}} is still in the first quadrant.