Question

if sinA =4/5,cos2A=?

Answer 1

use formula cos2a=1-2 sin^2a
we get cos2a=9/25

Answer 2

You need to apply the double angle formula for the sine:

 

sin(2A) = 2sin(A)cos(A)

 

Since sin(A) = 4/5:

 

sin(2A) = 2*(4/5)*cos(A) = (8/5)cos(A)

 

To find cos(A), use the Pythagorean identity:

 

sin2(A) + cos2(A) = 1

cos2(A) = 1 - sin2(A)

cos2(A) = 1 - (4/5)2

cos2(a) = 9/25

√cos2(A) = √(9/25)

 

cos(A) = ±3/5

 

So:

 

sin(2A) = (8/5)*(±3/5) = ±24/25

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