Question 755781: Find sin2x, cos2x, and tan2x if cos=4/5 and x terminates in quad iv.
I found that opp=3, hyp= 5, and adj=4. I am having trouble trying to figure out what exactly I need to show for the answers. For sin2x, I got as far as sin2x=2((3/5)(-4/5) but I am not sure if this is correct.
Thank you for viewing.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find sin2x, cos2x, and tan2x if cos=4/5 and x terminates in quad iv.
cosx=4/5
sinx=-3/5
tanx=-3/4
x in quadrant IV where cos>0, sin<0, and tan<0
..
Identities:
sin2x=2sinxcosx=2*(-3/5)(4/5)=-24/25
cos2x=1-2sin^2x=1-2*(-3/5)^2=1-18/25=7/25
tan2x=(2tanx)/(1-tan^2x)=(2*(-3/4)/(1-(-3/4)^2)=(-6/4)/(1-(9/16))=(-24/16)/(7/16)=-24/7
..
computer check:
cosx=4/5 (in Q4)
x≈360º-36.87º=323.13º
2x=646.26º
..
tan2x=tan(646.26º)≈-3.4246..
Exact value=-24/7≈-3.4286
..
cos2x=cos(646.26º)≈0.2799..
Exact value=7/25≈0.28
..
sin2x=sin(646.26º)≈-0.9600..
Exact value=-24/25≈-0.9600..
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