If sin(a)=(-4/5) and sec (b)=(5/3) for a third quadrant angle a and a first quadrant angle b, find the following...

Question

If sin(a)=(-4/5) and sec (b)=(5/3) for a third quadrant angle a and a first quadrant angle b, find the following...

(a) sin(a+b)

(b)tan(a+b)

Answer 1

sina = -4/5, cosa = -3/5, tan a = sina/cosa = 4/3

 

secb = 5/3, cosb = 1/secb = 3/5, sinb = 4/5 , tanb = 4/3

 

sin(a+b) = sinacosb + cosasinb = (-4/5)(3/5) + (-3/5)(4/5) = 

 

                                                        = -12/25 -12/25 = -24/25

 

tan(a + b) = [tana + tanb]/[1 - tanatanb]

 

                   = [4/3 + 4/3]/[1 - (4/3)(4/3)]

 

                   = (8/3)/[1 - 16/9]  

 

                   = (8/3)/(-7/9)  = -24/7