SOLUTION: Find the exact value of the trigonometric expression given that sin u =5/13 and cos v = −3/5 . (Both u and v are in Quadrant II.) tan(u + v)

Question 921229: Find the exact value of the trigonometric expression given that
sin u =5/13
and
cos v = −3/5
.
(Both u and v are in Quadrant II.)
tan(u + v)
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
sin u =5/13, cos u = -12/13 , tan u = -5/12
and
cos v = −3/5, sin v = 4/5 , tan v = -4/3
........
tan(u - v) = (tan u - tan v)/(1 + tan u tan v)
Let You finish Up
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let A = u and B = v

you have:

sine of A = 5/13
cosine of B = -3/5

both angles are in the second quadrant.

use the pythagorean formula to solve for the missing leg of each triangle.

you will get:

side opposite A = 5
side adjacent A = -12
hypotenuse A = 13

side opposite B = 4
side adjacent B = -3
hypotenuse B = 5

the side adjacent is negative in both triangles because they are both in the second quadrant where the value of x is negative while the value of y is positive.

now that you know the sides, you can solve for tangent of A and tangent of B.

tangent of A will be equal to 5 / -12 which is equal to -5/12.

tangent of B will be equal to 4 / -3 which is equal to -4/3.

tangent of A+B is equal to (tangent of A plus tangent of B) divided by (1 - tangent of A * tangent of B).

plug values in for the words and you get:

tangent of A plus B = ((-5/12) - (4/3)) divided by (1 - (-5/12 * -4/3)

do the arithmetic and this turns out to be:

tangent of A plus B = -1.75 / .4444444 which is equal to -3.9375.

that's your solution.

you can translate this back to u and v by letting u = A and v = B and you get:

tan(u+v) = -3.9375.

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SOLUTION: Find the exact value of the trigonometric expression given that sin u =5/13 and cos v = &#8722;3/5 . (Both u and v are in Quadrant II.) tan(u + v)

SOLUTION: Find the exact value of the trigonometric expression given that sin u =5/13 and cos v = −3/5 . (Both u and v are in Quadrant II.) tan(u + v)