Question

How do I solve:

Given:
csc θ = −(17/15), where 270° ≤ θ ≤ 360° and
cot β = −(3/4) where 90° ≤ β ≤ 180°.
Find the exact value of sin(θ + β).

Answer 1

csc θ = −(17/15)
=> 1/sinθ = −(17/15)
=> sinθ = -15/17
opp side= 15, hyp. =17
By Pyth Thm, we get adj. side =8
=> cos θ = 8/17 (since it is in quad IV)

cot β = −(3/4)
=> 1/tanβ = −(3/4)
=> tanβ = -4/3
opp. side =4, adj side =3,
By Pyth Thm, hyp. =5
=> sinβ = 4/5
cosβ = -3/5 (since it is in quadrant II)

sin(θ + β) = sinθ cosβ + cosθsinβ
= (-15/17) (-3/5) + ( 8/17)(4/5)
Can you do it now?

Answer 2

welcome :)

Answer 3

not really....

Answer 4

Yes :)

Answer 5

It should be :)

Answer 6

welcome :)

Answer 7

cos θ = adj side/ hyp
= 8/17
As it is in quad IV, so its value is positive

Answer 8

No problem. Once again, you're not bothering me :)