Given sin A 512 A E Q3 Find sin2ASolutionsinA512 opposite5

Given sin A -5/12 , A E Q3 Find sin(2A)

Solution

sinA=-5/12

opposite=5   and hypotenuse=12

Therefore adjacent= sqrt(hypotenuse²-opposite²)= sqrt119

And A is in third quadrant. Therefore cos A is negative

cos A= - sqrt119/12

sin 2A=2sin A cos A= 2(-5/12)(-sqrt119/12)= 10sqrt119/144= 5sqrt119/72