Question

DANGER! need help! please?
please help! crashing for finals!
find cos(u+v) given that sin u=3/5 and cos v=-5/13 (both u and v are in Quad 2

Answer 1

sin u = 3/5


sin^2 u = 9/25


1 - sin^2 u = 1 - 9/25


cos^2 u = 16/25


cos u = -4/5 ... Note: we're in quad II


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cos v = -5/13


cos^2 v = 25/169


1 - cos^2 v = 1 - 25/169


sin^2 v = 144/169


sin v = 12/13


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cos(u+v)


cos(u)cos(v)-sin(u)sin(v)


(-4/5)(-5/13)-(3/5)(12/13)


4/13-36/65


-16/65


So cos(u+v) = -16/65

Answer 2

i understand the first chunk that u typed but i got lost on that same part where u typed 1-sin^2 u=1-9/25 why did this have to be done?

Answer 3

I want to go from sin u to cos u

So I'm using the idea that sin^2 + cos^2 = 1 or 1 - sin^2 = cos^2

Answer 4

ahhhh okay but why is it necessary to change to cosine?

Answer 5

because cos(u+v) expands out to cos(u)cos(v)-sin(u)sin(v)

so I need to find cos(u) using the given sin(u)

Answer 6

I also needed to find sin(v) using the given cos(v)

Answer 7

hmm okay i c then that means that we have to get the sin(v) using the cos right?

Answer 8

exctly

Answer 9

exactly*

Answer 10

okay so i basically have to get the cos and sin given and get their opposites right and once i do that i add them>?

Answer 11

you multiply them out like I wrote above, then you subtract

Answer 12

o okay the original given cos and sin by the ones that were gathered right?

Answer 13

yes

Answer 14

YEAH! ALRIGHT I THINK I GOT THIS.. HEY IF U DON'T MIND....CAN U GIVE ME A COUPLE OF PROBLEMS TO PRACTICE ON MY OWN?

Answer 15

find cos(u+v) given sin(u) = 3/5 and cos(v) = 8/17 (both u and v are in Quad I)

Answer 16

OKAY THANK U I'LL USE IT TO PRACTICE LATER I APPRECIATE IT!

Answer 17

yw

Answer 18

:)