SOLUTION: exact value of sin 157.5 without using a calculator

Question 677446: exact value of sin 157.5 without using a calculator
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
exact value of sin 157.5 without using a calculator
sin(157.5)=sin(315/2)
Identity: sin(x/2)=�√[(1-cosx)/2]
select positive identity since 175 is in the 2nd quadrant where sin>0
sin(315/2)=√[(1-cos315)/2]
cos 315=cos45 in quadrant IV=√2/2
sin(315/2)=√[(1-√2/2)/2]=√[(2-√2)/4]=√(2-√2)/2
sin(157.5)=√(2-√2)/2
check using calculator:
sin157.5�≈0.382...
√(2-√2)/2≈0.382...
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