SOLUTION: Find the exact function value if cos x = 2/3, and 3pi/2 < x < 2pi, then find tan 2x

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Question 809920: Find the exact function value if cos x = 2/3, and 3pi/2 < x < 2pi, then find tan 2x
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the exact function value if cos x = 2/3, and 3pi/2 < x < 2pi, then find tan 2x.
Reference angle is in quadrant IV where cos>0, sin<0, tan<0
sin%28x%29=-sqrt%281-cos%5E2%28x%29%29=-sqrt%281-4%2F9%29=-sqrt%285%2F9%29=-sqrt%285%29%2F3
tan(x)=sin(x)/cos(x)=-√5/2
tan(2x)=2tan(x)/(1-tan^2(x))=-√5/(1-5/4)=-√5/(-1/4)=4√5
..
check: (w/calculator)
cos(x)=2/3
x≈311.8103˚
2x≈623.6206
tan(2x)≈tan(623.6206)≈8.9442..
exact value as calculated=4√5≈8.9442..