Question

sin α = 15/17 where π/2 < α < π

cos β= − 3/5 where π < β < 3π/2

cos θ= 7/25 where −2π < θ < −3π/2


(a) sin(α + β)= ?

(b) cos(α + β)= ?

I've tried every possible way to get the answer, but I end up with an incorrect solution.

Answer 1

need to use trig identities for sin(A+B) and cos(A+B)

Answer 2

\[\sin \left( \alpha+\beta \right)=\sin \alpha \cos \beta+\cos \alpha \sin \beta \]

Answer 3

\[\cos \left( \alpha+\beta \right)=\cos \alpha \cos \beta-\sin \alpha \sin \beta \]

Answer 4

\[\frac{ \pi }{ 2}<\alpha <\pi,\cos \alpha~is~negative.\]

Answer 5

I tried doing that and I still keep getting the wring answer, I don't know what I'm doing wrong.

Answer 6

wrong*

Answer 7

\[\pi <\beta<\frac{ 3 \pi }{ 2 },\sin \beta~is~negative\]

Answer 8

can you show me your work?

Answer 9

ok, so I've done (15/17) (-3/5) + (-5/17)(-4/5)= -45/85 + 20/85= -25/85

Answer 10

I don't know if that's the correct answer?

Answer 11

would you like help with this

Answer 12

Yes pleaaaaase.

Answer 13

sin α = 15/17 where π/2 < α < π this is 2nd quadrant

cos β= − 3/5 where π < β < 3π/2 this is third quadrant

cos θ= 7/25
where −2π < θ < −3π/2
this is equivalent to
(−2π+ 2π) < θ < (−3π/2 + 2π)
0 < θ < π / 2

(a) sin(α + β)= ?

(b) cos(α + β)= ?

Answer 14

are we using cos θ in this problem?

Answer 15

nope.

Answer 16

that was extra?

Answer 17

basically it was part of the question. The problem mainly focuses on the first two equations.

Answer 18

use a =α , and b = β

sin(a) = 15/17
cos(a) = -8 / 17 <--- show this using unit circle

cos (b)= -3/5
sin(b) = -4/5

sin(a + b) = sin(a) cos(b) + cos(a) (sin b)
= 15/17 *(-3/5) + (-8)/17 *(-4/5) = -13/85

Answer 19

Not exactly a unit circle, lets say a circle with radius 17

Answer 20

Oh. I found the answer for the second half, it's 84/85. Thank you for your help!

Answer 21

you can use pythagorean theorem to find the unknown side of that triangle