## anonymous 5 years ago http://locker.palcs.org/~jbaskwill/pc/5-4practice.pdf need help with 1-10 except #2

1. anonymous

1) cosx=sin2x cosx = 2sinx cosx 0 = 2sinx cosx - cosx 0 = cosx(2sinx-1) 2sinx-1 = 0 OR cosx = 0 2sinx=1 x = 90, 270 sinx =1/2 sinx=sin30 or sinx=sin(180-30) x =30 or x=150 answer : C

2. anonymous

3) sin2x=-sinx 2sinx cosx = -sinx 2sinxcosx + sinx = 0 sinx(2cosx +1) = 0 2cosx +1=0 OR sinx=0 2cosx =-1 x = 0, 180 cosx = -1/2 cosx = cos(180-60) OR cosx = cos (180+60) x = 120 x = 240 the value of cosx will be negative if it's located in quadrant 2 and 3 answer : A

3. anonymous

4) 2cosx + sin2x = 0 this isn't much different number 1 and 3 try to do it by yourself :)

4. anonymous

typo, i mean : number 4 isnt much different with number 1 and 3

5. anonymous

9) $\cos x = \sin (x/2)$ $1-2\sin ^{2}(x/2) = \sin(x/2)$ $2\sin ^{2}(x/2) + \sin(x/2) - 1 = 0$ (2sin(x/2) - 1)(sin(x/2)+1) = 0 sin(x/2) = 1/2 or sin(x/2) = -1 sin(x/2) = sin 30 sin(x/2) = sin270 x/2 = 30 x/2 = 270 x= 60 x = 540 -> this is out of interval OR sin(x/2) = 150 x=300 answer : A