SOLUTION: In this problem x means theta If tanx= -2/3. And x is in the second quadrant, use a double angle formula to find sin2x. In which quadrant is 2x?

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Question 817973: In this problem x means theta
If tanx= -2/3. And x is in the second quadrant, use a double angle formula to find sin2x. In which quadrant is 2x?
Answer by lwsshak3(11628) About Me  (Show Source):
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If tanx= -2/3. And x is in the second quadrant, use a double angle formula to find sin2x. In which quadrant is 2x?
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sin(2x)=2sin(x)cos(x)
reference angle(x)is in quadrant II where sin>0, cos<0, tan<0
hypotenuse of reference right triangle in quadrant II=√((2^2)+(3^2))=√(4+9)=√13
sin(x)=2/√13
cos(x)=-3/√13
sin(2x)=2*2√13*-3/√13=-12/13
..
calculator check:
tanx=-2/3
x≈146.31˚(in quadrant II)
2x≈292.62˚(in quadrant IV)
sin(2x)=sin(292.62)≈-0.923
exact value as calculated=-12/13≈-0.923
(2x) is in quadrant IV