SOLUTION: Find sin 2x, cos 2x, and tan 2x from the given information. csc x = 7, tan x

SOLUTION: Find sin 2x, cos 2x, and tan 2x from the given information. csc x = 7, tan x < 0

Question 955463: Find sin 2x, cos 2x, and tan 2x from the given information.
csc x = 7, tan x < 0

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 = 7, tan x < 0
***
Reference angle x is in quadrant II where sin>0, cos<0
sinx=1/cscx=1/7
cosx=-√1-sin^2(x)=-√(1-1/49)=-√(48/49)=-(√48)/7
sin2x=2*sinx*cosx=2*1/7*-√48/7=-2*√48/49
cos2x=cos^2(x)-sin^2(x)=48/49-1/49=47/49
tan2x=sin2x/cos2x=-2√48/47
Check:
w/calculator:
sinx=1/7
x≈171.79˚
2x≈343.5736˚
tan2x≈tan(343.57)≈-0.2948
exact value as computed=-2√48/47≈-0.2948
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