If cosx=2/3 abd x is in quadrant 4 find sin(x/2)

Question

a) -1/3

b) 1/3

c) - sqrt1/6

d) sqrt1/6

 

I think it is either c or d.  I'm confused on whether it is negative or positive.  If it is in quadrant 4, wouldn't y be negative?  C?

 

 

2) If tanx=-4/3 and x is in quadrant 2, then cos 2x=?

 

a) -7/25

b)7/25

c) -3/5

d)3/5

 

explain? 

Answer 1

cos(x)=2/3 in Q 4

sin(x/2)=+√(1-cos(x))/2

√(1-cos(x))/2=√(1-[2/3]/2=√(1/3)/2=-√(1/6) because sin is negative in Q 4

 

tan(x)=-4/3 in Q 2

cos(2x)=1-2sin²(x)

sin(x)=4/5 if tan(x)=4/3

1-2sin²(x)=1-2(4/5)²=1-2(16/25)=1-(32/25)=(25/25)-(32/25)=-7/25