An equation is given. (Enter your answers as a comma-separated list. Let k be an
ID: 2906097 • Letter: A
Question
An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. If there is no solution, enter NO SOLUTION.) 4 sin theta cos theta - 2squareroot 3 sin theta - 2squareroot 3 cos theta-3=0 Find all solutions of the equation. theta = Find the solutions in the interval (0, 2pi). theta = Find the product zxz^2 and the quotient . Express your answers in polar form. (Express theta in radians.) Zl = 3(cos9pi/8 + /Sin9pi/8.), z2 = 2(cospi/8 + /sinpi/8) z1z2 = z1/z2 = Write Z1 and z2 in polar form. (Express theta in radians. Let 0 LE thetaExplanation / Answer
1. 4sinxcosx +2sqrt3sinx -2sqrt3cosx -3 =0
2sinx(2cosx +sqrt3 ) -sqrt3( 2cosx +sqrt3) =0
(2sinx-sqrt3)(2cosx+sqrt3) =0
sinx = sqrt3/2 ;
General slution x= pi/3 +2pi*k ; x= 2pi/3 +2pi*k
cosx = -sqrt3/2
General solution : x= 5pi/6 +2pi*k ; x = 7pi/6 +2pi*k
b) solution between 0<=x <2pi
x = pi/3 , 2pi/3 , 5pi/6 , 7pi/6
cosx = -sqrt3/2