Question 955463
Find sin 2x, cos 2x, and tan 2x from the given information.
csc x = 7, tan x < 0
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Reference angle x is in quadrant II where sin>0, cos<0
sinx=1/cscx=1/7
cosx=-&#8730;1-sin^2(x)=-&#8730;(1-1/49)=-&#8730;(48/49)=-(&#8730;48)/7
sin2x=2*sinx*cosx=2*1/7*-&#8730;48/7=-2*&#8730;48/49
cos2x=cos^2(x)-sin^2(x)=48/49-1/49=47/49
tan2x=sin2x/cos2x=-2&#8730;48/47
Check:
w/calculator:
sinx=1/7
x&#8776;171.79&#730;
2x&#8776;343.5736&#730;
tan2x&#8776;tan(343.57)&#8776;-0.2948
exact value as computed=-2&#8730;48/47&#8776;-0.2948