Question

Find the value of sin(A/2) and cos(A/2). If sinA = -323/325 and A lies in 3rd quadrant ( Ps : pls dont take sin inverse and find the value. I want the steps. TY)

Answer 1

♠Answer♠

if SinA = -323\325

Then , CosA = -36\325

♠ we know , Cos2(Q) = 2Cos²Q - 1

So , Cos A = 2Cos²(A\2)-1
-36\325 +1 = 2Cos²(A\2)

Cos(A\2) = 17/√650
And ,
Cos A is also equal to

1-2Sin²(A\2 ) =-36\325

Sin(A\2) = 19\√650

Here are Your Answers !!

#SupermanINFINITY

♠Formulae Used :

SinA = √(1-Cos²A)

Cos2A = 2Cos²A-1 = 1-2Sin²A

Answer 2

hi friend,

given,sinA = -323/325

→by applying Pythagoras Theorem

we get cosA=-36/325

we know that

cosA=2cos²(A/2)-1



-36/325+1=2cos²(A/2)

289/325=2cos²A/2

289/650=cos²A/2


17/√650=cosA/2

we also know that

cosA=1-2sin²A/2

1+36/325=2sin²(A/2)

361/650=sin²(A/2)

sinA/2=19/√650

I hope this will help u :)