SOLUTION: If sin(x)= -4/5, on the interval (pi,3pi/2) find the exact value of tan2(x)

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Question 967994: If sin(x)= -4/5, on the interval (pi,3pi/2) find the exact value of tan2(x)
Answer by lwsshak3(11628) About Me  (Show Source):
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If sin(x)= -4/5, on the interval (pi,3pi/2) find the exact value of tan2(x)
reference angle x is in quadrant III where cos<0, sin<0
sinx=-4/5
cosx=-3/5
sin(2x)=2sinxcosx=2*-4/5*-3/5=24/25
cos(2x)=cos^2(x)-sin(^2(x)=9/25-16/25=-7/25
tan(2x)=sin(2x)/cos(2x)=-24/7
check:
sinx=-4/5 (Q3)
x=233.13
2x=106.26
tan(2x)=tan(466.26)≈3.4286
exact value as computed above=-24/7≈3.4386