Question

Question #122b2

Answer 1

`24/25`

Explanation:

Use the trig identity:
sin (a + b) = sin a.cos b + sin b.cos a
In this formula, we know sin a and sin b.
We must find cos a and cos b.
`sin a = 3/5`--> `cos^2 a = 1 - 9/25 = 16/25` --> `cos a = 4/5`(because a is in Quadrant I)
`sin b = 4/5` --> `cos^2 b = 1 - 16/25 = 9/25`--> `cos b = 3/5`(Quadrant 1)
Finally,
`sin (a + b) = (3/5)(4/5) + (3/5)(4/5) = 2(3/5)(4/5) = 24/25`