Question 924316: Find sin 2x, cos 2x, and tan 2x from the given information.
csc x = 6, tan x < 0
sin 2x =
cos 2x =
tan 2x =
please help
Thank you
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find sin 2x, cos 2x, and tan 2x from the given information.
csc x = 6, tan x < 0
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Reference angle x is in quadrant II where sin>0, cos<0
sinx=1/cscx=1/6
cosx=-√(1-sin^2(x))=-√(1-1/36)=-√(35/36)=-√35/6
..
sin(2x)=2sinxcosx=2*1/6*-√35/6=-2√35/36
cos(2x)=cos^2(x)-sin^2(x)=35/36-1/36=34/36
tan(2x)=sin(2x)/cos(2x)=-2√35/34
..
check:
sinx=1/6
x≈170.41
2x≈340.81
sin(2x)≈sin(340.81˚)=-0.3287
exact value as computed=-2√35/36≈-0.3287
..
cos(2x)=cos(340.81)≈0.9444
exact value as computed=34/36≈0.9444
..
tan(2x)=tan(340.81)≈-0.3480
exact value as computed=-2√35/34≈-0.3480
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