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

Solution

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

$sin a=\frac{4}{9}, sin b=\frac{2}{5},cos^2a=1 -sin^2 a=1-\frac{16}{81}=\frac{65}{81}\\\\cos a=\frac{\sqrt{65}}{9}, cos^2 b=1 -sin^2 b=1-\frac{4}{25}\\\\ cos b=\frac{\sqrt{21}}{5}\\\\ sin(a+b)=sin a *cos b+ cos a* sin b\\\\ sin(a+b)=\frac{4}{9}*\frac{\sqrt{21}}{5}+\frac{2}{5}*\frac{\sqrt{65}}{9}\\\\=\frac{4*\sqrt{21}+2*\sqrt{65}}{45}$

Used the Identity

sin²a+cos²a=1

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