SOLUTION: 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

SOLUTION: 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

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
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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
***
#1
cos(x)=4/5
sin(x)=3/5 (3-4-5) right triangle
tan(x)=sin(x)/cos(x)=3/4
...
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
..
#2
sin(x)=1/3
adjacent side=√(3^2)-1)=√8
cos(x)=√8/3
tan(x)=1/√8=√8/8=√2/4
...
sin(2x)=2sin(x)cos(x)=2*1/3*√8/3=2√8/9
cos(2x)=cos^2(x)-sin^2(x)=8/9-1/9=7/9
tan(2x)=(2tan(x))/(1-tan^2(x))=(√2/2)/(1-(1/8))=(√2/2)/(7/8)=4√2/7
..
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