Question 817973
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=&#8730;((2^2)+(3^2))=&#8730;(4+9)=&#8730;13
sin(x)=2/&#8730;13
cos(x)=-3/&#8730;13
sin(2x)=2*2&#8730;13*-3/&#8730;13=-12/13
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calculator check:
tanx=-2/3
x&#8776;146.31&#730;(in quadrant II)
2x&#8776;292.62&#730;(in quadrant IV)
sin(2x)=sin(292.62)&#8776;-0.923
exact value as calculated=-12/13&#8776;-0.923
(2x) is in quadrant IV