Question

find the value of sin2A when the sinA=12/13​

Answer 1

Answer:

sin ( 2 a ) = 120 /169

Step-by-step explanation:

sin ( a )  =  opposite  / hypotenuse

Adjacent  =  √ hypotenuse 2 − opposite 2

Replace the known values in the equation.

Adjacent = √ ( 13 ) 2 − ( 12 ) 2 Simplify  √ ( 13 ) 2 − ( 12 ) 2

Adjacent  = √ 169 − 144

Subtract  144  from  169

Adjacent  =  √ 25  

Rewrite  25  as  5 ^2

Adjacent  = √ 5 ^2

sin ( a )  =  opposite  / hypotenuse  sin

sin( a )  =  12 /13

apply 2 sin ( a ) cos ( a )

sin( a )  =  12 /13  and cos (a) = 5/13

so, sin(a) x cos(a)

Evaluate  

2 ( 12 /13 )  x 5 /13  to find  sin ( 2 a )

Combine  

2  and  12 /13 .

sin ( 2 a ) = 2 ⋅ 12 /13 x  5 /13

Multiply  2  by  12 .

sin ( 2 a ) = 24 /13  x  5/ 13

sin ( 2 a ) = 120 /169

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