Question

using the value of cos 315° find the values of sin 157 1/2° and cos 157 1/2°​

Answer 1

Answer:

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...