Question 867728
tan &#946; = 2, 180° < &#946; < 270°. Find the exact value of sin 2&#946; and cos 2&#946;
hypotenuse of reference right triangle={{{sqrt(2^2+1^2)=sqrt(4+1)=sqrt(5)}}}
{{{cos(beta)=-1/sqrt(5)}}}
{{{sin(beta)=-2/sqrt(5)}}}
{{{sin(2beta)=2sin(beta)cos(beta)=2*(-2/sqrt(5))*(-1/sqrt(5))=4/5}}} 
{{{cos(2beta)=cos^2(beta)-sin^2(beta)=1/5-4/5=-3/5}}}
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Calculator check:
tan(B)=2
B=243.435(in quadrant III)
2B&#8776;486.87(in quadrant II)
sin(2B)=sin(486.87)&#8776;0.7999…
Exact value as calculated=4/5=0.8000
cos(2B)=cos(486.87&#8776;-0.6000…
Exact value as calculated=-3/5=-0.6000