trignometry

Question

find cos (a+b) if sin (a) = -3/5 where a is in the fourth quardrant and tan (b) =12/5 where b is in the third quardrant

Answer 1

We can use the addition angle identity for cosine.

 

cos(a)cos(b) - sin(a)sin(b)

 

 

We already know sin(a).  We need to find cos(a), cos(b) and sin(b) using other trig identities.

 

cos(a) = √[1 - sin²(a)]

          = √[1 - (9/25)]

          = √[(25 - 9)/25]

          = √(16/25)

cos(a) = 4/5

 

 

sec²(b) = 1 + tan²(b)

           = 1 + (144/25)

           = (25 + 144) / 25

           = 169/25

 

1 / cos²(b) = 169/25

cos²(b) = 25/169

 

cos(b) = - 5/13

 

 

 

Then

 

sin(b) = √[1 - (25/169)]

sin(b) = √[(169 - 25)/169]

 

sin(b) = - √(145/169)

 

sin(b) = - √(145) / 13

 

 

You know have all the values you need just plug them into the identity and simplify.