Question

Find exact value given that secx = 3/2, cscy = 3, and x and y are in Quadrant I.

sin(x+y)

Answer 1

So far I have \[\frac{ 2\sqrt{10} }{ 3 }+\frac{ 2 }{ 9 }\]

Answer 2

you got a bunch of work to do

Answer 3

\[\sin(x+y)=\sin(x)\cos(y)+\cos(x)\sin(y)\]

Answer 4

at the moment you know
\[\cos(x)=\frac{2}{3}\] and
\[\sin(y)=\frac{1}{3}\]

Answer 5

you need two more numbers,
\[\sin(x)\] and
\[\cos(y)\]

Answer 6

sin x = sqrt(5)/3 and cos y = 2sqrt(2)/3

Answer 7

ok then you are in good shape
plug them in and you are done

Answer 8

you know all four numbers for
\[\sin(x)\cos(y)+\cos(x)\sin(y)\]

Answer 9

I did. But I don't know where to go from 2sqrt10/3 + 2/9

Answer 10

lets see

Answer 11

\[\frac{\sqrt5}{3}\times \frac{2\sqrt2}{3}+\frac{2}{3}\times \frac{1}{3}\]
\[=\frac{2\sqrt{10}+2}{9}\] if my arithmetic is correct

Answer 12

Yes, you're right. I did mine wrong.

Answer 13

i think you made a mistake in the denominator of the first part

Answer 14

other than that it is correct

Answer 15

Awesome, thanks

Answer 16

yw