Question 961906
find the exact values of sin 2a, cos 2a, and tan 2a when tan a = 2, &#960; < a < 3&#960;/2
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reference angle a is in quadrant III where sin<0, cos<0
hypotenuse of reference right triangle in quadrant III=&#8730;(2^2+1^2)=&#8730;5
sina=2/&#8730;5=(2&#8730;5)/5
cosa=1/&#8730;5=&#8730;5/5
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sin 2a=2sinacosa=2*(2&#8730;5)/5*&#8730;5/5=20/25=4/5
cos2a=cos^2a-sin^2a=5/25-20/25=-15/25=-3/5
tan2a=sin2a/cos2a=-4/3
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Check: w/calculator
tan a=2 (Q3)
a=243.4349&#730;
2a=486.87&#730;
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sin2a&#8776;sin(486.87)&#8776;0.7999...
exact value as computed=4/5=0.8
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cos2a&#8776;cos(486.87)&#8776;-0.6000...
exact value as computed=-3/5=-0.6
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tan2a&#8776;tan(486.87)&#8776;-1.3333...
exact value as computed=-4/3=-1.3333...