Question

Find the exact value of the trigonometric expression given that
sin u =8/17 and cos v = −15/13
(Both u and v are in Quadrant II.)

sin(u + v)

Answer 1

it is impossible for cosine to be equal to \(-\frac{15}{13}\)
did you mean \(-\frac{12}{13}\)?

Answer 2

@satellite73 I copied it exactly how it was written.

Answer 3

@3mar This is the one that I am talking about

Answer 4

then it is a mistake
cosine cannot be smaller than \(-1\)

Answer 5

you got a screen shot or something to look at ?

Answer 6

This is a screenshot

Answer 7

hmm entirely different question

Answer 8

@satellite73 I posted a screenshot above

Answer 9

that is something about tangent, not the question you posted above

Answer 10

Sorry I uploaded the wrong one, hold on

Answer 11

ok holding
i bet $7 it is \(-\frac{12}{13}\)

Answer 12

@satellite73

Answer 13

ok l lose
but it is \(-\frac{5}{13}\) not \(-\frac{15}{13}\) whew

Answer 14

now we can do it

Answer 15

\[\sin(u+b)=\sin(u)\cos(v)+\sin(v)\cos(u)\] you already know two out of the four numbers, you need the other two

Answer 16

You just wrote exactly the same numbers

Answer 17

in inglish
minus five over thirteen, not minus fifteen over thirteen

Answer 18

Do you mean sin(u+V)=sin(u)cos(v)+sin(v)cos(u) ?

Answer 19

@satellite73 is right!
It is not logic and not what we know!

Answer 20

yes
you know two out of the four, you need the other two

Answer 21

Yes

Answer 22

\[\sin(u)=\frac{8}{17}\] what is \(\cos(u)\)?

Answer 23

or is that what you need help finding?

Answer 24

Yes, I am not really here how to get the cos

Answer 25

draw a right triangle is one easy way to do it

Answer 26

there is a picture of an angle whose sine is \(\frac{8}{17}\)
what you need is the "adjacent" side, which you find via pythagoras

Answer 27

So 15 for the other side

Answer 28

yes, and therefor \[\cos(u)=-\frac{15}{17}\] negative because they told you you were in quadrant II

Answer 29

Why would it be negative though?

Answer 30

oh sorry just read it

Answer 31

lol

Answer 32

now we repeat the process to find \(\sin(v)\) given that \(\cos(v)=-\frac{5}{13}\)

Answer 33

12/5 ?

Answer 34

no that is tangent
the 12 is right though

Answer 35

opposite over hypotenuse

Answer 36

Wait 5/13 sorry

Answer 37

no, that was what you were given, cosine
you want sine

Answer 38

12/13

Answer 39

yes

Answer 40

now plug the numbers in and do the arithmetic, that is all that is left to do

Answer 41

\[\sin(u+v)=\sin(u)\cos(v)+\sin(v)\cos(u)\] you now know all four numbers on the right

Answer 42

Okay I am working on it

Answer 43

ok
arithmetic is sometimes annoying

Answer 44

How do you simplify it though? Do you need common denominators?

Answer 45

if by "simplify" you mean find the number, yes, but you don't need to find a common denominator in this case because the denominators are equal

Answer 46

But it is split by a + sign so I can't just add the common terms together

Answer 47

the denominator of both the fraction on the right and the fraction on the left is \(13\times 17=221\)

Answer 48

what did you write down to compute?

Answer 49

\[\sin \frac{ 8 }{ 17 } \cos-\frac{ 5 }{ 13} + \sin \frac{ 12 }{ 13 } \cos-\frac{ 15 }{ 17 }\]

Answer 50

hmm i was afraid of that

Answer 51

it is not the sine OF \(\frac{8}{17}\)
the sine IS \(\frac{8}{17}\)

Answer 52

\[ \frac{ 8 }{ 17 } \times -\frac{ 5 }{ 13} + \frac{ 12 }{ 13 } \times -\frac{ 15 }{ 17 }\]

Answer 53

those numbers ARE the sine and cosine of u and v
you do not take the sine and cosine OF those numbers
just compute with the numbers

Answer 54

What does compute mean? Sorry for asking

Answer 55

find the number? multiply and add i guess

Answer 56

perhaps what i really meant was "do the arithmetic"

Answer 57

\[-\frac{ 40 }{ 221 }+\] \[\frac{ 180 }{ 221}\]

Answer 58

-220/221 ?

Answer 59

looks right to me