Question 748758: Find the exact values of sin 2a, cos 2a, and tan 2a.
tan a=2, pi < a < 3pi/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.
tan a=2, pi < a < 3pi/2
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tan(a)=2
hypotenuse=√(2^2+1)=√5
sin(a)=-2/√5
cos(a)=-1/√5
..
sin(2a)=2sin(a)cos(a)=2*-2/√5*-1/√5=4/5
cos(2a)=cos^2(a)-sin^2(a)=1/5-4/5=-3/5
tan(2a)=(2tan(a))/(1-tan^2(a))=4/(1-4)=-4/3
..
computer check:
tan(a)=2
a=243.13º (in quadrant III)
2a=486.86º-360=126.86º(in quadrant II)
reference angle=126.86-180=53.13º
..
sin(2a)=sin(53.1º)≈0.799...
exact value=4/5=0.800
..
cos(2a)=cos(53.1º)≈-0.600...
exact value=-3/5=-0.600
..
tan(2a)=tan(53.1º)≈-1.331...
exact value=-4/3=-1.333...
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