SOLUTION: If the cos x is -(1/2) and the x is in the 2nd quadrant, find the cos 2x. (no calculator) I have been working on this problem for 30 mins. I think I am missing one thing for it

Question 816468: If the cos x is -(1/2) and the x is in the 2nd quadrant, find the cos 2x. (no calculator)
I have been working on this problem for 30 mins. I think I am missing one thing for it to make sense. I think that sin x= 2/sq.rt. 5...
Show that this is a trig identity.
csc^2 = cot^2x+1
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
If the cos x is -(1/2) and the x is in the 2nd quadrant, find the cos 2x.
cos(2x)=cos^2(x)-sin^2(x)
..
cos(x)=(-1/2)
cos^2(x)=1/4
..
sin(x)=√3/2
sin^2(x)=3/4
..
cos(2x)=(1/4)-(12/16)=(4/16)-(12/16)=-8/16=-1/2
...
Show that this is a trig identity.
csc^2x = cot^2x+1
start with right side:
cot^2x+1=cos^2/sin^2x+1
(sin^2(x)+cos^2(x))/sin^2(x)
1/sin^2(x)=csc^2(x)
verified:
right side=left side

RELATED QUESTIONS
sin 2x + cos 60 = 0, 0 < x < 360. i have been able to find out that sin inverse of -1/2 (answered by stanbon,Theo)

Question: TanA = v; A is in Quadrant 1. Obtain Sin2A and Cos2A. My work so far:... (answered by Edwin McCravy)

Find sin (2x), cos (2x), and tan (2x) from the given information. tan (x) = 1/2 x... (answered by lwsshak3)

Solve the equation for x, on the interval 0 is less than or equal to x and 2pi is greater (answered by Alan3354)

In my pre ap geometry class, we have been working with tan, sin, and cos to find angles... (answered by josmiceli)

Hello, I've been working on this problem for about an hour and I'm having a very hard... (answered by greenestamps)

Find cos(x/2) if sinx=_3/4 and x is the third... (answered by josmiceli)

if sinx=-3/4 and x is the third quadrant find cos(x/2) (answered by Theo)

Find sin(2x), cos(2x), and tan(2x) from the given information. cot(x) = 2/3, x in... (answered by Alan3354)