<span>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: sin157.5º≈0.382... √(2-√2)/2≈0.382...</span>
