Question 924316
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=-&#8730;(1-sin^2(x))=-&#8730;(1-1/36)=-&#8730;(35/36)=-&#8730;35/6
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sin(2x)=2sinxcosx=2*1/6*-&#8730;35/6=-2&#8730;35/36
cos(2x)=cos^2(x)-sin^2(x)=35/36-1/36=34/36
tan(2x)=sin(2x)/cos(2x)=-2&#8730;35/34
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check:
sinx=1/6
x&#8776;170.41
2x&#8776;340.81
sin(2x)&#8776;sin(340.81&#730;)=-0.3287
exact value as computed=-2&#8730;35/36&#8776;-0.3287
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cos(2x)=cos(340.81)&#8776;0.9444
exact value as computed=34/36&#8776;0.9444
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tan(2x)=tan(340.81)&#8776;-0.3480
exact value as computed=-2&#8730;35/34&#8776;-0.3480