Question

http://locker.palcs.org/~jbaskwill/pc/5-4practice.pdf

need help with 1-10 except #2

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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