SOLUTION: Find sin(x/2), cos(x/2), and tan(x/2) from the given information. tan(x)= 2sqrt6 and 0^degrees < x < 90^degrees

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Question 869336: Find sin(x/2), cos(x/2), and tan(x/2) from the given information.
tan(x)= 2sqrt6 and 0^degrees < x < 90^degrees
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find sin(x/2), cos(x/2), and tan(x/2) from the given information.
tan(x)= 2sqrt6 and 0^degrees < x < 90^degrees
tan%28x%29=2sqrt%286%29
hypotenuse of reference right triangle in quadrant I=sqrt%28%282sqrt%286%29%29%5E2%2B1%29=sqrt%2824%2B1%29=sqrt%2825%29=5%29
sin%28x%29=2sqrt%286%29%2F5
cos%28x%29=1%2F5
..
=2√10/10=√10/5
=√(3/5)
tan(x/2)=sin/cos=(√10/5)/√(3/5)=√50/5√3
..
Calculator check:
tan(x)=2√6
x≈78.46
x/2≈39.23˚
..
sin(x/2)≈sin 39.23≈0.6324
exact value as calculated=√10/5≈0.6324
..
cos(x/2)≈cos 39.23≈0.7746
exact value as calculated=√(3/5)≈0.7746
..
tan(x/2)=tan 39.23≈0.8164
exact value as calculated=√50/(5√3)≈0.8164