Question 748251
Use the given information to find sin 2theta, cos 2theta, and tan 2theta.
#1) cos theta = 4/5 , 0 deg < theta < 90 deg 
#2) sin theta = 1/3, 0 < theta < pi/2
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#1
cos(x)=4/5
sin(x)=3/5 (3-4-5) right triangle
tan(x)=sin(x)/cos(x)=3/4
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sin(2x)=2sin(x)cos(x)=2*3/5*4/5=24/25
cos(2x)=cos^2(x)-sin^2(x)=16/25-9/25=7/25
tan(2x)=(2tan(x))/(1-tan^2(x)=(6/4)/(1-(9/16))=(24/16)/(7/16)=24/7
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#2
sin(x)=1/3
adjacent side=&#8730;(3^2)-1)=&#8730;8
cos(x)=&#8730;8/3
tan(x)=1/&#8730;8=&#8730;8/8=&#8730;2/4
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sin(2x)=2sin(x)cos(x)=2*1/3*&#8730;8/3=2&#8730;8/9
cos(2x)=cos^2(x)-sin^2(x)=8/9-1/9=7/9
tan(2x)=(2tan(x))/(1-tan^2(x))=(&#8730;2/2)/(1-(1/8))=(&#8730;2/2)/(7/8)=4&#8730;2/7
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