Question

Given sinu=4/5, with u in quadrant 1, and cosv=7/25, with v in quadrant 1, Find cos(u+v)

Here are the choices
A) (-3/5)
B) (-44/125)
C) (117/125)
D) (4/5)

Answer 1

hint:

cos(u+v) = cos(u)cos(v) - sin(u)sin(v)

Answer 2

so you'll need to know the values of cos(u) and sin(v)

Answer 3

still confused....

Answer 4

if sin(u) = 4/5, then what is cos(u) ?

Answer 5

well wouldn't they just be the same?

Answer 6

no they aren't

Answer 7

they how are they different

Answer 8

have you seen the identity

\[\Large \cos^2(u) + \sin^2(u) = 1\]

??

Answer 9

yes

Answer 10

so because sin(u) = 4/5, we can square both sides to get sin^2(u) = 16/25

which means

\[\Large \cos^2(u) + \sin^2(u) = 1\]

\[\Large \cos^2(u) + \frac{16}{25} = 1\]

now isolate cos(u)

Answer 11

cosu= 3/5

??

Answer 12

correct

Answer 13

now if cos(v)=7/25, then what is sin(v) ?

Answer 14

24/25

???

Answer 15

good

Answer 16

so we have these 4 facts

sin(u) = 4/5
cos(u) = 3/5

cos(v) = 7/25
sin(v) = 24/25

Answer 17

you plug them into the right side of

cos(u+v) = cos(u)cos(v) - sin(u)sin(v)

to compute cos(u+v)

Answer 18

Is the answer A) -3/5
????

Answer 19

no

Answer 20

oh wait, one sec

Answer 21

yes sorry, I had the wrong values in my calculator

Answer 22

cos(u+v) = -3/5

Answer 23

great thank you

Answer 24

you're welcome