Question 961906: find the exact values of sin 2a, cos 2a, and tan 2a when tan a = 2, π < a < 3π/2
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find the exact values of sin 2a, cos 2a, and tan 2a when tan a = 2, π < a < 3π/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=√(2^2+1^2)=√5
sina=2/√5=(2√5)/5
cosa=1/√5=√5/5
..
sin 2a=2sinacosa=2*(2√5)/5*√5/5=20/25=4/5
cos2a=cos^2a-sin^2a=5/25-20/25=-15/25=-3/5
tan2a=sin2a/cos2a=-4/3
..
Check: w/calculator
tan a=2 (Q3)
a=243.4349˚
2a=486.87˚
..
sin2a≈sin(486.87)≈0.7999...
exact value as computed=4/5=0.8
..
cos2a≈cos(486.87)≈-0.6000...
exact value as computed=-3/5=-0.6
..
tan2a≈tan(486.87)≈-1.3333...
exact value as computed=-4/3=-1.3333...
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