SOLUTION: Find sin(x/2), cos(x/2), and tan(x/2) from the given information
tan(x)=2; 0 degrees< x <90 degrees
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Question 236926: Find sin(x/2), cos(x/2), and tan(x/2) from the given information
tan(x)=2; 0 degrees< x <90 degrees
Answer by Alan3354(69443) (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)=2; 0 degrees< x <90 degrees
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tan = 2
tan^2 = 4
----------
sin^2/(1-sin^2) = 4
sin^2 = 4 - 4sin^2
5sin^2 = 4
sin^2 = 4/5
sin(x) = 2sqrt(5)/5
------------
cos^2 = 1/5
cos(x) = sqrt(5)/5
------------
------------
Do 1/2 angles
sin(x/2) = sqrt((1 - cos(x)/2)
sin(x/2) = sqrt((1 - sqrt(5)/5)/2)
sin(x/2) = sqrt(0.5 - sqrt(5)/10)
---------------------------------
cos(x/2) = sqrt((1 + cos(x)/2)
sin(x/2) = sqrt((1 + sqrt(5)/5)/2)
sin(x/2) = sqrt(0.5 + sqrt(5)/10)
---------------------------------
tan(x/2) = sin(x)/(1 + cos(x))
tan(x/2) = 0.4sqrt(5)/(1 + sqrt(5)/5)
tan(x/2) = 2sqrt(5)/(5 + sqrt(5))
tan(x/2) = 2sqrt(5)*(5 - sqrt(5))/20
tan(x/2) = 0.5sqrt(5) - 0.5
tan(x/2) = (sqrt(5) - 1)/2
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