Question

Find the exact value of the trig expression given that sin u = -5/13 and cos v = -4/5. u and v are in the second quadrant.

cos(v - u)

Is this -33/65?

Answer 1

@SolomonZelman

Answer 2

how is angle u in the second quadrant but they state that `sin u = -5/13` ??

Answer 3

sine is positive in Q2

Answer 4

Typo...only cos is negative. The sin is positive.

Answer 5

so it says sin(u) = 5/13 ?

Answer 6

yes

Answer 7

ok one sec

Answer 8

-33/65 is incorrect

Answer 9

You can use a difference of two angles formula for cosine (you can find an explanation here: http://www.intmath.com/analytic-trigonometry/2-sum-difference-angles.php )

\(\cos(v-u)=\cos{v} \cos{u} + \sin{v} \sin{u} \)

Plug in the values that you are given, \(\cos{v}=-\dfrac{4}{5}\) and \(\sin{u}=-\dfrac{5}{13}\)
Then using special right triangles, you can figure out the two remaining quantities, \(\cos{u}\) and \(\sin{v}\)

Answer 10

Where's the mistake?

Answer 11

We wouldn't know, you didn't show your work.

Answer 12

yes please post your work/steps

Answer 13

cosvcosu + sinvsinu

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

-48/65 + 15/65
= -33/65

Answer 14

since angle u is in the second quadrant, cos(u) should be negative

Answer 15

I think sin u can be negative

Answer 16

sin(u) is positive

Answer 17

sin(u) = 5/13
cos(u) = -12/13


sin(v) = 3/5
cos(v) = -4/5

Answer 18

-4/5(-12/13)
= 48/65

48/65 + 15/65 = 63/65

Answer 19

correct

Answer 20

Thanks to both of you!

Answer 21

btw this is extra trivia I guess but cos(v - u) = cos(u-v) because


cos(u-v) = cos(-1*(-u+v))
cos(u-v) = cos(-(v-u)))
cos(u-v) = cos(v-u) ... using the property that cos(-x) = cos(x)


and you're welcome