4 3. Find the exact value of tan (u+v) given that sin u=9/41and cos v = 15/17. (

Question

4

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

4. Using half-angle formulas, find the exact value of cos/2 given the following constraints.

cos=12/13,   <<32

4

1. Write the following expression as an algebraic expression in for

.

2. If

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

4. Using half-angle formulas, find the exact value of cos/2 given the following constraints.

cos=12/13,   <<32

Explanation / Answer

1) cos ( sin^-1 x/ sqrt ( x^2 + 64 )

let ( sin^-1 x/ sqrt ( x^2 + 64 ) = y

sin y = x/ sqrt ( x^2 + 64 )

perpendicular = x

hypotenuse = sqrt ( x^2 + 64 )

base = sqrt ( x^2 + 64 - x^2 ) = 8

cos y = base / hypotenuse = 8 / sqrt ( x^2 + 64 )

hence, cos ( sin^-1 x/ sqrt ( x^2 + 64 ) =  8 / sqrt ( x^2 + 64 )

2) sin theta = 2/7

perpendicular = 2

hypotenuse = 7

base = sqrt (7^2 - 2^2 )

base = sqrt 45

cos theta = - sqrt 45 / 7

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