Question

Can someone help me out with this Trig question? When sinx = -8/17 and x lies in Quadrant III and cosy = -4/5 and y lies in Quadrant II, what is cos(x-y?)

So far, I did cos(-8/17 - -4/5) =

cos-8/17cos-4/5 + sin-8/17sin-4/5

And now I'm stuck.

Answer 1

we need
\[\cos(x-y)=\cos(x)\cos(y)+\sin(x)\sin(y)\] so we want
\[\cos(x), \sin(x), \cos(y), \sin(y)\]

Answer 2

I think so.

Answer 3

\[\sin(x)=-\frac{8}{17}\]

Answer 4

sorry that was a type, but before we start let me point out something i think is confusing youi

Answer 5

the sine of x IS -8/17, you do not want the sine of -8/17
you just need these numbers, not the sine or cosine of these numbers

Answer 6

cos(x) = -15/17, you wanted that earlier, right?

Answer 7

So... I'm not supposed to be using the formula I used...?

Answer 8

yes, but you are confused i think about the formula.
you need the numbers themselves, not the cosine and sine of the numbers

Answer 9

in other words just work with the numbers

\[\sin(x)=-\frac{8}{15}\]
\[\cos(x)=-\frac{15}{17}\]
\[\cos(y)=-\frac{4}{2}\]
\[\sin(y)=\frac{3}{5}\]

Answer 10

typo there
\[\cos(y)=-\frac{4}{5}\] of course
now plug the numbers directly into the formula

Answer 11

and in quadrant II sine is positive

Answer 12

so your answer is
\[-\frac{8}{17}\times -\frac{4}{5}+(-\frac{15}{17})\times \frac{4}{5}\]

Answer 13

clear right? those are the sines and cosines, you do not take the sines and cosines of those numbers

Answer 14

Uh... I'm a little confused, hold on a sec x_x;;;

Answer 15

ok i will wait. this is a common mistake, i have seen it before

Answer 16

point is that
\[\cos(x)=-\frac{3}{5}\] you do not take the cosine of that number. that number is your cosine

Answer 17

If it's cos(x)cos(y), shouldn't it be -15/17 x -4/5?

Answer 18

yes sorry that was a typo on my part

Answer 19

you are right
just don't do this
cos-8/17cos-4/5 + sin-8/17sin-4/5

instead do this

-8/17 *-4/5 + -8/17*4/5

Answer 20

According to my calculator, that's zero, unless there's another typo ><....

Answer 21

no it is not zero