Question

if a and b are the measures of two first quadrant angles and sin a = 4/9 and sin b = 2/5 find sin (a+b)

Answer 1

38/45. 49+25 =( 4 × 5) + (2 × 9) 9 × 5 = 38/45

Answer 2

it is given that ,a and b are the measures of two first quadrant angles and sin a = 4/9 and sin b = 2/5

`sin a=(4)/(9), sin b=(2)/(5),cos^2a=1 -sin^2 a=1-(16)/(81)=(65)/(81)\\\\cos a=(√(65))/(9), cos^2 b=1 -sin^2 b=1-(4)/(25)\\\\ cos b=(√(21))/(5)\\\\ sin(a+b)=sin a *cos b+ cos a* sin b\\\\ sin(a+b)=(4)/(9)*(√(21))/(5)+(2)/(5)*(√(65))/(9)\\\\=(4*√(21)+2*√(65))/(45)`

Used the Identity

sin²a+cos²a=1

sin (a+b)=sin a cos b+cos a sin b