SOLUTION: Find the exact value of sin(t/2) if csc(t)=5/4 and t is an acute angel?? Please show work all the way out. So confused!

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Question 762238: Find the exact value of sin(t/2) if csc(t)=5/4 and t is an acute angel?? Please show work all the way out. So confused!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of sin(t/2) if csc(t)=5/4 and t is an acute angle?
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sin%28t%2F2%29=sqrt%28%281-cos%28t%29%29%2F2%29%29
csc(t)=5/4
sin(t)=4/5
cos(t)=3/5 (working with 3-4-5 right triangle)
sin%28t%2F2%29=sqrt%28%281-%283%2F5%29%2F2%29%29
sin%28t%2F2%29=sqrt%28%282%2F5%29%2F2%29%29
sin%28t%2F2%29=sqrt%282%2F10%29=sqrt%2820%29%2F10
Calculator check:
sin(t)=4/5
t≈53.13º
t/2≈26.565º
sin(t/2)≈sin(26.565º)º≈0.4472
exact value=√20/10≈0.4472