document.write( "Question 748251: Use the given information to find sin 2theta, cos 2theta, and tan 2theta.
\n" ); document.write( "#1) cos theta = 4/5 , 0 deg < theta < 90 deg\r
\n" ); document.write( "\n" ); document.write( "#2) sin theta = 1/3, 0 < theta < pi/2 \n" ); document.write( "
Algebra.Com's Answer #455496 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
Use the given information to find sin 2theta, cos 2theta, and tan 2theta.
\n" ); document.write( "#1) cos theta = 4/5 , 0 deg < theta < 90 deg
\n" ); document.write( "#2) sin theta = 1/3, 0 < theta < pi/2
\n" ); document.write( "***
\n" ); document.write( "#1
\n" ); document.write( "cos(x)=4/5
\n" ); document.write( "sin(x)=3/5 (3-4-5) right triangle
\n" ); document.write( "tan(x)=sin(x)/cos(x)=3/4
\n" ); document.write( "...
\n" ); document.write( "sin(2x)=2sin(x)cos(x)=2*3/5*4/5=24/25
\n" ); document.write( "cos(2x)=cos^2(x)-sin^2(x)=16/25-9/25=7/25
\n" ); document.write( "tan(2x)=(2tan(x))/(1-tan^2(x)=(6/4)/(1-(9/16))=(24/16)/(7/16)=24/7
\n" ); document.write( "..
\n" ); document.write( "#2
\n" ); document.write( "sin(x)=1/3
\n" ); document.write( "adjacent side=√(3^2)-1)=√8
\n" ); document.write( "cos(x)=√8/3
\n" ); document.write( "tan(x)=1/√8=√8/8=√2/4
\n" ); document.write( "...
\n" ); document.write( "sin(2x)=2sin(x)cos(x)=2*1/3*√8/3=2√8/9
\n" ); document.write( "cos(2x)=cos^2(x)-sin^2(x)=8/9-1/9=7/9
\n" ); document.write( "tan(2x)=(2tan(x))/(1-tan^2(x))=(√2/2)/(1-(1/8))=(√2/2)/(7/8)=4√2/7
\n" ); document.write( ".. \n" ); document.write( "
\n" );