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