1. ## Double Angle ID issues, did my teacher grade wrong?

If Sin X = -4/5 and X is in Quadrant 4, then find Cos 2X

I have used the Double Angle ID and I got -7/25 as my answer.

However, here is where my problem is at. The question says that X is in Q4, so therefore Cos has to be positive right?

This was a question that I did on my Trig test and I got it wrong...the choices were...

A. -24/25
B. -7/25
C. 24/25
D. 7/25

I chose D because Cos is positive in Q4, however the correct answer was B, the exact same answer I got when I used the double angle formula...but it says X is in Q4????

Can somebody explain this to me please? Thanks!

2. Originally Posted by iAlphaBeasti
If Sin X = -4/5 and X is in Quadrant 4, then find Cos 2X

I have used the Double Angle ID and I got -7/25 as my answer.

However, here is where my problem is at. The question says that X is in Q4, so therefore Cos has to be positive right?

This was a question that I did on my Trig test and I got it wrong...the choices were...

A. -24/25
B. -7/25
C. 24/25
D. 7/25

I chose D because Cos is positive in Q4, however the correct answer was B, the exact same answer I got when I used the double angle formula...but it says X is in Q4????

Can somebody explain this to me please? Thanks!
cos 2x = 1 - 2sin^2 x
= 1 - 2(-4/5)2
= 1 - 32/25
= -7/25

cos x would be positive in Q4 but cos 2x is a different proposition

If x is in Q4 then 2x is in Q3 or Q4

3. Originally Posted by Glaysher
cos 2x = 1 - 2sin^2 x
= 1 - 2(-4/5)2
= 1 - 32/25
= -7/25

cos x would be positive in Q4 but cos 2x is a different proposition

If x is in Q4 then 2x is in Q3 or Q4
what do you mean different proposition? could you elaborate it a little bit more?

4. Originally Posted by iAlphaBeasti
what do you mean different proposition? could you elaborate it a little bit more?
Cos (angle) is positive if the angle in is Q4

You only know that x is in Q4 ie 270 - 360 degrees so cos x is positive

But 2x would range between 540 (180) and 720 (360) degrees putting 2x in either Q3 or Q4 depending on what the original x actually was

And Cos (angle) is negative if the angle is in Q3

5. Originally Posted by Glaysher
Cos (angle) is positive if the angle in is Q4

You only know that x is in Q4 ie 270 - 360 degrees so cos x is positive

But 2x would range between 540 (180) and 720 (360) degrees putting 2x in either Q3 or Q4 depending on what the original x actually was

And Cos (angle) is negative if the angle is in Q3
Yeah but it could also be positive if it was in Q4 like you say so how would I know which choice to choose? sorry for all the questions.

6. Originally Posted by iAlphaBeasti
Yeah but it could also be positive if it was in Q4 like you say so how would I know which choice to choose? sorry for all the questions.
It could have been postive without doing the working out but when we applied the cos 2x formula we got a negative answer fixing 2x in Q3

cos 2x = 1 - 2sin^2 x
= 1 - 2(-4/5)^2
= 1 - 32/25
= -7/25

However if the question had said sin x = -1/5 and x is in Q4 we would have got:

cos 2x = 1 - 2sin^2 x
= 1 - 2(-1/5)^2
= 1 - 2/25
= 23/25

and so in this specific case 2x would have been in Q4