Question

Find the exact value of cos (u-v) given that sin u=-9/41 and cos v=15/17. (Both u and v are in quadrant IV)

Answer 1

The exact value of cos(u-v) given sin u=-9/41 and cos v=15/17 in quadrant IV is -207/697.

Step-by-step explanation:

To find the exact value of cos(u-v), we can use the trigonometric identity cos(u-v) = cos u * cos v + sin u * sin v. Given that sin u = -9/41 and cos v = 15/17 in quadrant IV, we can substitute these values into the formula and solve.

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

= (-9/41) * (15/17) + (-9/41) * (8/17)

= -135/697 - 72/697

= -207/697

So, the exact value of cos(u-v) is -207/697.

Answer 2

Please review the sum and difference formulas for the trig functions.

In this case you have the difference between two angles u and v and want to find the cosine of this difference.

Here's the appropriate formula:

cos (a-b) = cos a cos b + sin a sin b

Given that sin u = -9/41, equal to the opp side over the hyp., we must find the length of the adj. side and then u itself.

opp side = - 9
hyp = 4
adj side = sqrt( 18+4) = sqrt(22)

Find the side opp angle v in a similar manner.

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

= (cos u)(15/17) + (-9/41)(sin v) (where you must find cos u and sin v)

See what you can do, then return and comment here if you need further help. Good luck.