Given: sin a=5/13 in Quadrant 1 and cos b=-12/13 in Quadrant 2; evaluate the following expression. sin(a+b)

1. -120/169
2. -1
3. 0

The answer to your question is 3. 0

Step-by-step explanation:

Process

1.- Find the cos a

   Opposite side = 5

   Hypotenuse = 13

   Adjacent side = ?

   Adjacent side² = 13² - 5²

                           = 169 - 25

                           = 144

  Adjacent side = 12

cos a = 12/13

2.- Find the sin b

 sin b = 5/13

3.- Use the formula below to find sin(a + b)

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

- Substitution

               sin (a + b) = (5/13)((-12/13) + (5/13)/12/13)

- Simplification

               sin (a + b) = -60/169 + 60/13

- Result

               sin(a + b) = 0