SOLUTION: If sin(theta)= (sqrt2)/5, and pi/2 < theta < pi, then find the exact value of tan(2theta) using identities (NO inverse trig, or SOHCAHTOA)

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Question 751293: If sin(theta)= (sqrt2)/5, and pi/2 < theta < pi, then find the exact value of tan(2theta) using identities (NO inverse trig, or SOHCAHTOA)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If sin(theta)= (sqrt2)/5, and pi/2 < theta < pi, then find the exact value of tan(2theta) using identities
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Identity: tan%282x%29=2tan%28x%29%2F%281-tan%5E2%28x%29%29
..
cos%28x%29=sqrt%281-sin%5E2%28x%29%29=sqrt%281-2%2F25%29=sqrt%2823%2F25%29
sec%28x%29=1%2Fcos%28x%29=sqrt%2825%2F23%29
Identity: tan%28x%29=sqrt%28sec%5E2%28x%29-1%29=sqrt%2825%2F23-1%29=sqrt%282%2F23%29

..
Check with calculator:
sin(x)=√2/5
x≈16.43º
2x≈32.86º
tan(2x)=tan(32.86º)≈0.6459
exact value=2sqrt%282%2F23%29%2F%2821%2F23%29≈0.6459