Question

41&43

In Problems 41-46, use the given information and appropriate identities to find the exact value of the indicated expression. 41. Find sin(x + y) if sin x = 1/3, cos y = -3/4, x is in quadrant II, and y is in quadrant III. 42. Find sin(x - y) if sin x = -2/5, sin y = 2/3, x is in quadrant IV, and y is in quadrant I. 43. Find cos(x - y) if tan x = -1/4, tan y = -1/5, x is in quadrant II, and y is in quadrant IV.

Answer 1

Aus- sincrty) = ? sinn = 1/3 cosy=-3 slw wl x is in thd y is in Tird quadrant quadrant sin, А и cosec We know that sinha + cos²n = 1 cos2n-1-sinan cos²x = 1- ( 2 = 1- tow, cos sec sot cosa = + 3 in I ho quadrant cosan negative so cosa= - Jol

similarly sinry=i-cosy =-(-? 21- Sinky I siny=fa yis in Tird quadrant where sin is negative sing = - - 7

Formula sinanty) = sinn cosy + cosn siny -)(-2) + (50) (-) sin(n+y) = 556-3 12 Ans 43 Coscn-y) = ? tann - I tany = - 1 sina= perpendicular hypotenuse hypotenuse = (1)2+(4,2 1 +16 AB = 17 sinn = I xis in and quadrant wher sin is positive cosna base cosa hypotemuseo cosx = -1 I cosin negative in ned quadrant similarly sing- cosy = 2 / 2 PQ2 = ( 1 ) ² + (512 = 1 +25 P Q = 526 sinne siny Formula Coscn-y) = Cosa cosy + = 1 - 1 / 1 ) 1 526 ) + ( 57 ) ( 3 ) = TGX26 57x526 Cos(21-4) = = June