Given sin(alpha)=4/9 and pi/2<alpha<pi, find the exact value of sin(alpha/2)

Reeves 2021-03-09 Answered

Given sin(α)=49andπ/2<α<π,
find the exact value of sin(α/2).

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Expert Answer

davonliefI
Answered 2021-03-10 Author has 79 answers

Step 1
π2<α<π
π22<α2<π2
π4<α2<π2
So, α2 in forst quadrant.
In first quadrant sin is positive.
Step 2 sin(α2)=1cosα2
So, we have to find cos alpha from sinα
π2<α<π is second quadrant.
There cosα is negative
cosα=1sin2α=1(49)2=11681=659
Step 3
Plug cosα=659 in the formula
sin(α2)=1cosα2
sin(α2)
=1(659)2
=1+6592
=9+6518
Multiply numerator and denominator by 2
=2(9+65)18(2)
=18+26536
=13+2135+56
=(13+5)26
=13+56
Answer: =13+56

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