SOLUTION: Given Tan x= 2/5 with &#960; < x < 3&#960;/2 find sin x/2 cos x/2 tan x/2 sin 2x cos 2x and tan 2x

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Question 860242: Given Tan x= 2/5 with π < x < 3π/2
find sin x/2 cos x/2 tan x/2
sin 2x cos 2x and tan 2x
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Given Tan x= 2/5 with π < x < 3π/2
find sin x/2 cos x/2 tan x/2
sin 2x cos 2x and tan 2x
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Reference right triangle is in quadrant III in which sin<0, cos<0, tan>0
Hypotenuse=√(2^2+5^2)=√(4+25)=√29
sin(x)=-2/√29
cos(x)=-5/√29
...
sin%28x%2F2%29=sqrt%28%281-cos%28x%29%29%2F2%29=sqrt%28%281%2B5%2Fsqrt%2829%29%29%2F2%29
cos%28x%2F2%29=sqrt%28%281%2Bcos%28x%29%29%2F2%29=sqrt%28%281-5%2Fsqrt%2829%29%29%2F2%29


cos%282x%29=cos%5E2%28x%29-sin%5E2%28x%29=25%2F29-4%2F29=21%2F29
tan%282x%29=sin%282x%29%2Fcos%282x%29=20%2F21
Note: Let me know if my solution(s) are correct, helpful and understandable.